Detailed Sudoku solution example, based
on method of elimination.

Note that the solution to this problem
requires use of extended chains of logic
that may appear indistinguishable from
trial-and-error to the casual sudoku
enthusiast.

Notation:
 there are 81 squares, denoted by two
 digits representing the row and column
 respectively. (E.g. square 32 is 7.)
 
 There are 9 boxes, numbered one to
 nine reading left-to-right-and-top-to-bottom.
 (E.g. Box 7 contains a 3, 7 and 9.)
 
 A fully determined digit is surrounded
 by asterisks.
 
 Numeric possibilities ("pencilmarks") are
 noted in a 3x3 arrangement in each square.

++===+===+===++===+===+===++===+===+===++
||***|   |   ||   |   |   ||***|   |   ||
||*6*|   |   ||   |   |   ||*2*|   |   ||
||***|   |   ||   |   |   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||   |   |   ||   |***|   ||   |***|***||
||   |   |   ||   |*1*|   ||   |*4*|*8*||
||   |   |   ||   |***|   ||   |***|***||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***|   |***||   |   |   ||
||   |*7*|   ||*9*|   |*5*||   |   |   ||
||   |***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|   |   ||   |   |***||   |   |   ||
||*2*|   |   ||   |   |*8*||   |   |   ||
||***|   |   ||   |   |***||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||   |   |***||   |   |   ||***|   |   ||
||   |   |*7*||   |   |   ||*1*|   |   ||
||   |   |***||   |   |   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||   |   |   ||***|   |   ||   |   |***||
||   |   |   ||*3*|   |   ||   |   |*6*||
||   |   |   ||***|   |   ||   |   |***||
++===+===+===++===+===+===++===+===+===++
||   |   |   ||***|   |***||   |***|   ||
||   |   |   ||*1*|   |*4*||   |*8*|   ||
||   |   |   ||***|   |***||   |***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|   ||   |***|   ||   |   |   ||
||*7*|*9*|   ||   |*6*|   ||   |   |   ||
||***|***|   ||   |***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||   |   |***||   |   |   ||   |   |***||
||   |   |*3*||   |   |   ||   |   |*5*||
||   |   |***||   |   |   ||   |   |***||
++===+===+===++===+===+===++===+===+===++

Filling in all possible numbers...

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 | 89||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
|| 5 | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***| 8 ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||456|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||456|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||1  |1  |1  ||***| 2 |12 ||   | 2 |***||
||4  |45 |45 ||*3*|45 |   ||45 | 5 |*6*||
|| 89| 8 | 89||***|7 9|7 9||789|7 9|***||
++===+===+===++===+===+===++===+===+===++
||   | 2 | 2 ||***| 23|***||  3|***| 23||
|| 5 | 56| 56||*1*| 5 |*4*||  6|*8*|   ||
||   |   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|12 || 2 |***| 23||  3|123|123||
||*7*|*9*|45 || 5 |*6*|   ||4  |   |4  ||
||***|***| 8 || 8 |***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |12 |***|| 2 | 2 | 2 ||   |12 |***||
||4  |4 6|*3*||   |   |   ||4 6|  6|*5*||
|| 8 | 8 |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked 5 in square 71 eliminates 5 in
square 7, row 7, and column 1

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 | 89||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***| 8 ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||456|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||456|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||1  |1  |1  ||***| 2 |12 ||   | 2 |***||
||4  |45 |45 ||*3*|45 |   ||45 | 5 |*6*||
|| 89| 8 | 89||***|7 9|7 9||789|7 9|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***| 23|***||  3|***| 23||
||*5*|  6|  6||*1*|   |*4*||  6|*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|12 || 2 |***| 23||  3|123|123||
||*7*|*9*|4  || 5 |*6*|   ||4  |   |4  ||
||***|***| 8 || 8 |***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |12 |***|| 2 | 2 | 2 ||   |12 |***||
||4  |4 6|*3*||   |   |   ||4 6|  6|*5*||
|| 8 | 8 |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked pair 26 in squares 72 and 73
eliminates 2 and 6 elsewhere in row 7
and box 7.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 | 89||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***| 8 ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||456|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||456|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||1  |1  |1  ||***| 2 |12 ||   | 2 |***||
||4  |45 |45 ||*3*|45 |   ||45 | 5 |*6*||
|| 89| 8 | 89||***|7 9|7 9||789|7 9|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|1  || 2 |***| 23||  3|123|123||
||*7*|*9*|4  || 5 |*6*|   ||4  |   |4  ||
||***|***| 8 || 8 |***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   |12 |***||
||4  |4  |*3*||   |   |   ||4 6|  6|*5*||
|| 8 | 8 |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Hidden 5 in row 8 eliminates 2 and 8 from
that square, and eliminates 5 in column 4.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 | 89||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***| 8 ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||4 6|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||1  |1  |1  ||***| 2 |12 ||   | 2 |***||
||4  |45 |45 ||*3*|45 |   ||45 | 5 |*6*||
|| 89| 8 | 89||***|7 9|7 9||789|7 9|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|1  ||***|***| 23||  3|123|123||
||*7*|*9*|4  ||*5*|*6*|   ||4  |   |4  ||
||***|***| 8 ||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   |12 |***||
||4  |4  |*3*||   |   |   ||4 6|  6|*5*||
|| 8 | 8 |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Hidden 8 in row 8.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||4 6|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||1  |1  |1  ||***| 2 |12 ||   | 2 |***||
||4  |45 |45 ||*3*|45 |   ||45 | 5 |*6*||
|| 89| 8 |  9||***|7 9|7 9||789|7 9|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   |12 |***||
||4  |4  |*3*||   |   |   ||4 6|  6|*5*||
||   |   |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked pair 14 in squares 91 and 92
eliminates 1 in square 98 and 4 in
square 97.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||4 6|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||1  |1  |1  ||***| 2 |12 ||   | 2 |***||
||4  |45 |45 ||*3*|45 |   ||45 | 5 |*6*||
|| 89| 8 |  9||***|7 9|7 9||789|7 9|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   | 2 |***||
||4  |4  |*3*||   |   |   ||  6|  6|*5*||
||   |   |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Hidden 1 in column 6 and hidden 8 in
column 7.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|456|456||4 6|45 |*8*||45 | 5 |4  ||
||***|   |  9||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||4  |456|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 89| 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |   |   ||***| 2 |***||***| 2 |***||
||4  |45 |45 ||*3*|45 |*1*||*8*| 5 |*6*||
||  9|   |  9||***|7 9|***||***|7 9|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   | 2 |***||
||4  |4  |*3*||   |   |   ||  6|  6|*5*||
||   |   |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked triplet 459 in squares 61, 62 and 63
eliminates 4, 5 and 9 from square 4 and
row 6.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|1 3|1 3||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||  3|***|***||
||   | 5 | 5 ||  6|*1*|  6|| 56|*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||1 3|***|12 ||***| 23|***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4 6|45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||   |  6|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |   |   ||***| 2 |***||***| 2 |***||
||4  |45 |45 ||*3*|   |*1*||*8*|   |*6*||
||  9|   |  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   | 2 |***||
||4  |4  |*3*||   |   |   ||  6|  6|*5*||
||   |   |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked triple 136 in squares 37, 38 and 39.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|45 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   | 5 | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4 6|45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||   |  6|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |   |   ||***| 2 |***||***| 2 |***||
||4  |45 |45 ||*3*|   |*1*||*8*|   |*6*||
||  9|   |  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||1  |1  |***|| 2 | 2 | 2 ||   | 2 |***||
||4  |4  |*3*||   |   |   ||  6|  6|*5*||
||   |   |***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Hidden 1 in square 91, leads to naked 4
in square 92.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*| 5 |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   | 5 | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4 6|45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||   |  6|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |   |   ||***| 2 |***||***| 2 |***||
||4  | 5 |45 ||*3*|   |*1*||*8*|   |*6*||
||  9|   |  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked 5 in square 62

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4 6|45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||   |  6|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Forcing chain beginning in square 42
ends in contradiction: if square 42 is
a 3, then square 12 must be 1, so
square 31 must be 8, so square 51 must
be 3, which contradicts the original
assumption that square 42 is a 3.
Eliminate 3 from square 42.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4 6|45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||   |  6|*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked pair 16 in squares 42 and 43.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 23| 23||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

Naked pair 38 in squares 51 and 52.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|7 9|***||
++===+===+===++===+===+===++===+===+===++

If square 65 is a 2, then square 68
must be 7, so square 98 would not
contain a 7.  If square 65 is not a 2,
then it is 7, and then only row 9
in box 8 can have 7s, so square 98
cannot have a 7 in that case either.
Conclusion is that square 98 may not
contain a 7.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*||45 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||  3|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||4  |   |4  ||
||***|***|***||***|***|   ||   |   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Contradiction if square 87 is a 3.
If square 87 is a 3, then squares 77 and 79
form a naked pair, such that square 97
must be a 6.  Unfortunately, if square 87
is a 3, then square 37 must be a 6, which
implies that square 97 cannot be a 6.
Therefore square 87 may not be 3.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|  9||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Eliminated either way: if square 16 is
a 7, then square 19 must be a 9, so
square 59 cannot be a 9.  If square 16 is
a 3, then square 86 must be 2, so square
89 cannot be 2, which leaves a hidden 2
in square 59, which again precludes a 9
being there.  Either way, cannot have a 9
in square 59.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***| 8 |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++


Contradiction if square 12 is an 8: implies
square 52 is a 3, but also implies that
square 31 is 4, square 33 is 2,
square 22 is a 3, which contradicts the
previous conclusion that square 52 is a 3.
So, square 12 cannot be an 8.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||   |***| 2 ||***| 2 |***||  3|1 3|1 3||
||4  |*7*|4  ||*9*|4  |*5*||  6|  6|   ||
|| 8 |***|   ||***| 8 |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
|| 8 | 8 |***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Hidden 8 in square 31.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3| 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||  3|  3|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||   |   |*7*||4 6|45 |  6||*1*| 5 |4  ||
||   | 8 |***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Naked 3 in square 51.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |  9||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||   | 23| 2 || 2 |***| 23||   |***|***||
||   |   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||  9|   |  9||7  |***|7  ||7 9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***|   |***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|   |*7*||4 6|45 |  6||*1*| 5 |4  ||
||***| 8 |***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||  9|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Naked 9 in square 21, naked 8 in square 52.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |   ||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|45 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||   |***|   ||***| 2 |***||***| 2 |***||
||4  |*5*|4  ||*3*|   |*1*||*8*|   |*6*||
||   |***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Naked 4 in square 61.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |   ||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|45 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|   ||***| 2 |***||***| 2 |***||
||*4*|*5*|   ||*3*|   |*1*||*8*|   |*6*||
||***|***|  9||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Naked 9 in square 63.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |   ||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  |45 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|45 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Regardless of value in square 65, 4 cannot
be in squares 45 or 55.  If square 65 is 2,
then square 35 will be 4. If it is 7, then
square 44 will be 4. Either way, 4 is
eliminated from squares 45 and 55.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||4  |4  |   ||*2*| 5 |   ||
||***|   |   ||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

4 occurs only in column 4 in block 5, so
it cannot occur elsewhere in column 4.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||   |4  |   ||*2*| 5 |   ||
||***|   |   ||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Regardless of the value in square 68,
square 49 cannot contain a 7.  Clearly,
if square 68 is 7, then square 49 cannot
have a 7.  Alternatively, if square 68
is a 2, then square 59 must be a 4, and
then column 9 has a hidden 2 in square 89,
so square 86 must have a 3, and square 16
must contain a 7, so square 18 cannot
contain a 7, which leaves a hidden 7 in
square 48, which means there can be no
7 in square 49.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |   ||
||*6*|   |45 ||   |4  |   ||*2*| 5 |   ||
||***|   |   ||78 |78 |7  ||***|7 9|7 9||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|  9||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|  3||
||*5*|  6|  6||*1*|   |*4*||   |*8*|   ||
||***|   |   ||***|7 9|***||7 9|***|7 9||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||7 9|  9|***||
++===+===+===++===+===+===++===+===+===++

Assuming square 19 is 7 leads to a
contradiction.  If square 19 is 7, then
square 27 must be 5, so square 23 must be 2,
so square 33 cannot be a 2, so square 35
must be a 2, so square 65 cannot be a 2,
so square 68 must be a 2, so square 59
cannot be a 2, and square 89 must be a 2.
Alternatively, if square 19 is a 7, then
square 16 must be a 3, so square 86 must
be a 2, so square 89 cannot be a 2.
Therefore square 19 cannot be 7, which leaves
a naked 9 and a hidden 7 in column 9.


++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |***||
||*6*|   |45 ||   |4  |   ||*2*| 5 |*9*||
||***|   |   ||78 |78 |7  ||***|7  |***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||  3|  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7 9|7 9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|  9|***||
++===+===+===++===+===+===++===+===+===++

Hidden pair 57 in boxes 27 and 47 eliminates
3 and 9 from box 47.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |***||
||*6*|   |45 ||   |4  |   ||*2*| 5 |*9*||
||***|   |   ||78 |78 |7  ||***|7  |***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||   |  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7  |7 9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|  9|***||
++===+===+===++===+===+===++===+===+===++

Digit 9 only appears in box 6 in column 8,
so it is eliminated from box 98.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |***||
||*6*|   |45 ||   |4  |   ||*2*| 5 |*9*||
||***|   |   ||78 |78 |7  ||***|7  |***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||   |  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7  |7 9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Having 2 in box 56 leads to a contradiction.
Box 56 as a 2 means box 86 is a 3, so box 75
is a 9, so box 96 cannot be a 9, but the
only other 9 in column 6 was in box 56,
so it cannot be a 2.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |***||
||*6*|   |45 ||   |4  |   ||*2*| 5 |*9*||
||***|   |   ||78 |78 |7  ||***|7  |***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||   |  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||7  |7 9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 |   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***| 2 |***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|   |*6*||
||***|***|***||***|7  |***||***|7  |***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

There are only two 2s left in column 9,
but regardless of which is the real 2,
square 68 cannot be a 2.  First, if square 59
is a 2, then square 68 cannot be a 2.
Alternately, if square 89 is a 2, then
square 86 must be a 3, so square 16 is
a 7, so square 18 cannot be a 7.  Returning
to square 86 being a 3, square 75 is a 9,
so square 45 can't be a 9, which creates
a naked pair 57 in squares 45 and 47, so
square 48 cannot contain a 7.  These two
alternatives mean that the 7 in square 68
must be a 7 (not a 2).

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|   |***||
||*6*|   |45 ||   |4  |   ||*2*| 5 |*9*||
||***|   |   ||78 |78 |7  ||***|   |***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6|| 5 |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***| 2 |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||   |  3|  3||
||*2*|  6|  6||4  | 5 |*8*|| 5 | 5 |4  ||
||***|   |   ||7  |7 9|***||   |  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 |   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*| 5 |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***| 2 |***||***|***|***||
||*4*|*5*|*9*||*3*|   |*1*||*8*|*7*|*6*||
||***|***|***||***|   |***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 | 2 | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 5 in square 18, naked 5 in square 47,
naked 2 in square 65.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|***|***||
||*6*|   |4  ||   |4  |   ||*2*|*5*|*9*||
||***|   |   ||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||   |***|***||
||*9*|   | 5 ||  6|*1*|  6||   |*4*|*8*||
||***|   |   ||7  |***|7  ||7  |***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***|   |***||  3|1 3|1 3||
||*8*|*7*|4  ||*9*|4  |*5*||  6|  6|   ||
||***|***|   ||***|   |***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||***|  3|  3||
||*2*|  6|  6||4  |   |*8*||*5*|   |4  ||
||***|   |   ||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |   |   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*|   |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 7 in square 27 and naked 4 in 
square 35.

++===+===+===++===+===+===++===+===+===++
||***|1 3|1  ||   |  3|  3||***|***|***||
||*6*|   |4  ||   |   |   ||*2*|*5*|*9*||
||***|   |   ||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***| 23| 2 || 2 |***| 23||***|***|***||
||*9*|   | 5 ||  6|*1*|  6||*7*|*4*|*8*||
||***|   |   ||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***| 2 ||***|***|***||  3|1 3|1 3||
||*8*|*7*|   ||*9*|*4*|*5*||  6|  6|   ||
||***|***|   ||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||***|  3|  3||
||*2*|  6|  6||4  |   |*8*||*5*|   |4  ||
||***|   |   ||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |   |   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*|   |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 2 in square 23, hidden 4 in row 1.

++===+===+===++===+===+===++===+===+===++
||***|1 3|***||   |  3|  3||***|***|***||
||*6*|   |*4*||   |   |   ||*2*|*5*|*9*||
||***|   |***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|  3|   || 2 |***| 23||***|***|***||
||*9*|   | 5 ||  6|*1*|  6||*7*|*4*|*8*||
||***|   |   ||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|1 3|1 3||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|   ||
||***|***|***||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|1  |1  ||   |   |***||***|  3|  3||
||*2*|  6|  6||4  |   |*8*||*5*|   |4  ||
||***|   |   ||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |   |   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*|   |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 | 2 ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 3 in square 22, naked 5 in square 23,
hidden 1 in row 1.

++===+===+===++===+===+===++===+===+===++
||***|***|***||   |  3|  3||***|***|***||
||*6*|*1*|*4*||   |   |   ||*2*|*5*|*9*||
||***|***|***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|1 3|1 3||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|   ||
||***|***|***||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|   |1  ||   |   |***||***|  3|  3||
||*2*|  6|  6||4  |   |*8*||*5*|   |4  ||
||***|   |   ||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |   |   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6| 5 |  6||*1*|   |4  ||
||***|***|***||   |  9|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***| 2 |   ||***|  3|***||  3|***|***||
||*5*|  6|  6||*1*|   |*4*||   |*8*|*7*||
||***|   |   ||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 6 in square 42, hidden 1 in row 4,
naked 6 in square 73, hidden 2 in row 7,
hidden 5 in row 5.

++===+===+===++===+===+===++===+===+===++
||***|***|***||   |  3|  3||***|***|***||
||*6*|*1*|*4*||   |   |   ||*2*|*5*|*9*||
||***|***|***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|1 3|1 3||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|   ||
||***|***|***||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|123|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

There are three 2's in column 8, but
regardless of the value found in square
98, there cannot be a 2 in square 88.
If square 98 is a 2, then square 88 cannot
be a 2.  If square 98 is a 6, then
square 97 must be a 9, and square 77 must
be a 3, and square 75 must be a 9, and
square 45 must be a 7, so square 44 must
be a 4, so square 54 must be a 6, so
square 56 must be a 9, so square 58
must be a 2, and square 88 again cannot
be a 2.

++===+===+===++===+===+===++===+===+===++
||***|***|***||   |  3|  3||***|***|***||
||*6*|*1*|*4*||   |   |   ||*2*|*5*|*9*||
||***|***|***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|1 3|1 3||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|   ||
||***|***|***||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|1 3|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |789|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

There are three 9s in column 5, but regardless
of the value in square 98, 9 cannot appear
in square 95.  If square 98 is 6, then
square 97 must be 9, so square 95 cannot
be 9. Alternatively, if square 98 is 2, then
square 58 must be 9, so square 56 cannot be 9,
so square 45 must be 9 and again square 95
cannot be 9.

++===+===+===++===+===+===++===+===+===++
||***|***|***||   |  3|  3||***|***|***||
||*6*|*1*|*4*||   |   |   ||*2*|*5*|*9*||
||***|***|***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|1 3|1 3||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|   ||
||***|***|***||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|1 3|123||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|   |   ||
||***|***|***||***|***|   ||***|   |   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |78 |7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Regardless of the value in square 98,
square 88 cannot contain a 3. First, if
square 98 is a 6, then square 97 must be 9,
so square 77 must be 3, so square 88
cannot be 3.  Alternatively, if square
98 is 6, then square 97 must be 9,
square 77 must be 3, square 75 must be 9,
square 45 must be 7, square 44 must be 4,
square 49 must be 3, square 39 must be 1,
and square 38 must be 3 (since the original
assumption eliminates 6 from that square),
which means that again square 88 cannot be 3.

++===+===+===++===+===+===++===+===+===++
||***|***|***||   |  3|  3||***|***|***||
||*6*|*1*|*4*||   |   |   ||*2*|*5*|*9*||
||***|***|***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|1 3||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|   ||
||***|***|***||***|***|***||   |   |   ||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |78 |7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked pair in squares 37 and 38.

++===+===+===++===+===+===++===+===+===++
||***|***|***||   |  3|  3||***|***|***||
||*6*|*1*|*4*||   |   |   ||*2*|*5*|*9*||
||***|***|***||78 |78 |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||78 |78 |7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Contradiction arises if we assume square 14
contains a 7.  If it is 7, then square 16
cannot be 7, which leaves a hidden 7 in
square 96, so square 95 must be 8, but
we have now surrounded square 15 with a 7,
a 3, and an 8, which is impossible, so
square 14 must not be 7.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|  3||***|***|***||
||*6*|*1*|*4*||*8*|   |   ||*2*|*5*|*9*||
||***|***|***||***|7  |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |   | 2 ||   | 2 |***||
||*1*|*4*|*3*||   |   |   ||  6|  6|*5*||
||***|***|***||7  |78 |7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Hidden 8 in row 9.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|  3||***|***|***||
||*6*|*1*|*4*||*8*|   |   ||*2*|*5*|*9*||
||***|***|***||***|7  |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||   | 2 |***||
||*1*|*4*|*3*||   |*8*|   ||  6|  6|*5*||
||***|***|***||7  |***|7 9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Regardless of the value in square 86,
square 96 cannot contain a 7.  If square 86
is a 2, then square 94 must be 7, so square 96
cannot be 7.  Alternatively, if square 86
is 3, then square 16 must be 7, and again
square 96 cannot be 7.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|  3||***|***|***||
||*6*|*1*|*4*||*8*|   |   ||*2*|*5*|*9*||
||***|***|***||***|7  |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||7  |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||   | 2 |***||
||*1*|*4*|*3*||   |*8*|   ||  6|  6|*5*||
||***|***|***||7  |***|  9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Hidden 7 in row 9.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|  3||***|***|***||
||*6*|*1*|*4*||*8*|   |   ||*2*|*5*|*9*||
||***|***|***||***|7  |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||   |   |***||***|  3|  3||
||*2*|*6*|*1*||4  |   |*8*||*5*|   |4  ||
||***|***|***||   |7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||4 6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 2 ||   | 2 |***||
||*1*|*4*|*3*||*7*|*8*|   ||  6|  6|*5*||
||***|***|***||***|***|  9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 4 in square 44.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|  3||***|***|***||
||*6*|*1*|*4*||*8*|   |   ||*2*|*5*|*9*||
||***|***|***||***|7  |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|   |***||***|  3|  3||
||*2*|*6*|*1*||*4*|   |*8*||*5*|   |   ||
||***|***|***||***|7 9|***||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||   |***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||  6|*5*|  6||*1*|   |4  ||
||***|***|***||   |***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 23||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 2 ||   | 2 |***||
||*1*|*4*|*3*||*7*|*8*|   ||  6|  6|*5*||
||***|***|***||***|***|  9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 6 in square 54, naked 3 in square 49.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|  3||***|***|***||
||*6*|*1*|*4*||*8*|   |   ||*2*|*5*|*9*||
||***|***|***||***|7  |7  ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|   |***||***|   |***||
||*2*|*6*|*1*||*4*|   |*8*||*5*|   |*3*||
||***|***|***||***|7 9|***||***|  9|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|   ||***| 2 | 2 ||
||*3*|*8*|*7*||*6*|*5*|   ||*1*|   |4  ||
||***|***|***||***|***|  9||***|  9|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 2 ||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 2 ||   | 2 |***||
||*1*|*4*|*3*||*7*|*8*|   ||  6|  6|*5*||
||***|***|***||***|***|  9||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 9s in squares 56 and 48, and naked
2 in column 9, and hidden 7s in row 4 and
column 6, and hidden 4 in row 5.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||***|***|***||
||*6*|*1*|*4*||*8*|   |*7*||*2*|*5*|*9*||
||***|***|***||***|   |***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***| 2 ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*2*|*6*|*1*||*4*|*7*|*8*||*5*|*9*|*3*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***| 2 |***||
||*3*|*8*|*7*||*6*|*5*|*9*||*1*|   |*4*||
||***|***|***||***|***|***||***|   |***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|  3|***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 23||***|***| 2 ||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|   ||
||***|***|***||***|***|   ||***|***|   ||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***| 2 ||   | 2 |***||
||*1*|*4*|*3*||*7*|*8*|   ||  6|  6|*5*||
||***|***|***||***|***|   ||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 3 in row 1, naked 2 in row 5 and
column 9 and square 96.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*6*|*1*|*4*||*8*|*3*|*7*||*2*|*5*|*9*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***|   ||***|***|***||
||*9*|*3*|*5*||  6|*1*|  6||*7*|*4*|*8*||
||***|***|***||   |***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|  6|*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*2*|*6*|*1*||*4*|*7*|*8*||*5*|*9*|*3*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*3*|*8*|*7*||*6*|*5*|*9*||*1*|*2*|*4*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|   |***||  3|***|***||
||*5*|*2*|*6*||*1*|   |*4*||   |*8*|*7*||
||***|***|***||***|  9|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|  3||***|***|***||
||*7*|*9*|*8*||*5*|*6*|   ||*4*|*1*|*2*||
||***|***|***||***|***|   ||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||   |   |***||
||*1*|*4*|*3*||*7*|*8*|*2*||  6|  6|*5*||
||***|***|***||***|***|***||  9|   |***||
++===+===+===++===+===+===++===+===+===++

Naked 9 in square 75, naked 3 in square 86,
and naked 6s in square 98 and square 26.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*6*|*1*|*4*||*8*|*3*|*7*||*2*|*5*|*9*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***|| 2 |***|***||***|***|***||
||*9*|*3*|*5*||   |*1*|*6*||*7*|*4*|*8*||
||***|***|***||   |***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||  3|  3|***||
||*8*|*7*|*2*||*9*|*4*|*5*||  6|   |*1*||
||***|***|***||***|***|***||   |   |***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*2*|*6*|*1*||*4*|*7*|*8*||*5*|*9*|*3*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*3*|*8*|*7*||*6*|*5*|*9*||*1*|*2*|*4*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||  3|***|***||
||*5*|*2*|*6*||*1*|*9*|*4*||   |*8*|*7*||
||***|***|***||***|***|***||  9|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*7*|*9*|*8*||*5*|*6*|*3*||*4*|*1*|*2*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||   |***|***||
||*1*|*4*|*3*||*7*|*8*|*2*||   |*6*|*5*||
||***|***|***||***|***|***||  9|***|***||
++===+===+===++===+===+===++===+===+===++

Naked 2 in square 24, naked 3 in square 38,
and naked 9 in square 97, and hidden 6
in row 3, and hidden 3 in row 7.

++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*6*|*1*|*4*||*8*|*3*|*7*||*2*|*5*|*9*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*9*|*3*|*5*||*2*|*1*|*6*||*7*|*4*|*8*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*8*|*7*|*2*||*9*|*4*|*5*||*6*|*3*|*1*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*2*|*6*|*1*||*4*|*7*|*8*||*5*|*9*|*3*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*3*|*8*|*7*||*6*|*5*|*9*||*1*|*2*|*4*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*4*|*5*|*9*||*3*|*2*|*1*||*8*|*7*|*6*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++
||***|***|***||***|***|***||***|***|***||
||*5*|*2*|*6*||*1*|*9*|*4*||*3*|*8*|*7*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*7*|*9*|*8*||*5*|*6*|*3*||*4*|*1*|*2*||
||***|***|***||***|***|***||***|***|***||
++---+---+---++---+---+---++---+---+---++
||***|***|***||***|***|***||***|***|***||
||*1*|*4*|*3*||*7*|*8*|*2*||*9*|*6*|*5*||
||***|***|***||***|***|***||***|***|***||
++===+===+===++===+===+===++===+===+===++