Chains with nets
 

Last resort AICs

The ultimate way to test the hypothesis that if a number is postulated to be false, and through logical alternating inferences another occurrence of the same number is found to be true elsewhere, is by generating a forcing net. Each unsolved number is put false in turn, and resulting true numbers are inspected to see if they include the starting number. If this is the case, any same number that can see both can be eliminated. Look at the following:

You get to this situation in Top95, #88, after several steps. The consequence of making the 1 at r1c9 negative is to make the 1 at r9c2 positive. Therefore, either the 1 at r1c9 is positive, but if it is not, the 1 at r9c2 is positive. So the 1 at r9c9 that sees them both can be removed. To understand how this works, enter "119" in the 'To see result of n=False,..'box and press 'Show True/False' button, and the following appears:

Note the 1 at r9c2 is red, ie true. The 1 at r8c9 is also true, but yields the same elimination. There are other red 1's, but they don't yield eliminations. Interestingly, making the 1 at r1c9 false leads to numerous contradictions (orange colour) so that the 1 at r1c9 must be true, so the 8 can also be eliminated.