8 {2,7} 6 {1,2} 3   5 9	4 9 5 8 7 6	{3,7}   1 5 9   8 6
4 5 3 {1,2} 6 9 7   8	1 6 8   4   5   9	2 7 9 {1,3} 5 8 4   6
3 4   6 8   9   5	6     9 5 3   8 4	9 8 5   4   6   3

 

(The numbers in curly brackets { } are the candidates for the cell.)

Consider r1c2. This has the two candidates, 2 and 7. We will consider the implications of each of these candidates in turn.

if r1c2 = 2, then r2c1 = 1, and r5c1 = 2

if r1c2 = 7, then r1c7 = 3, and r5c7 = 1, and r5c1 = 2

So whichever of the two possible values are placed into (1, 2), we've deduced that (5, 1) must hold a 2. In other words, whichever chain of cells we follow, a certain cell is forced to have a specific value.

Note: unless the puzzle has multiple solutions, one of the considered candidates must be incorrect. This means it must eventually lead to either a contradiction or a dead end. If, when considering a single candidate, you reach a dead end, or find two chains that lead to different conclusions, you can eliminate that candidate from the starting cell. This is verging on trial-and-error, this can be useful when solving manually.

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