Double Line/Box Reduction
This article is part two of the new
Double Intersection Removal strategy specifically for Jigsaw Sudoku puzzles. I recommend reading part one on
Double Pointing Pairs first. I am indebted to
Brain Hobson's observations for this excellent prod in the right direction and I am appreciating Jigsaws in a whole new way.
With
Line/Box Reduction we take one box and one line (a row or column) and look for a specific number that only exists in the overlap of that box and line. So by looking along a row you may see that all the 2s are in the same box (or shape). If that is the case we know the solution will be one of those cells - otherwise the row would lose that number altogether. From this idea we can remove the rest of those candidates from the box or shape in question.
With Jigsaw Puzzles we have shapes that overlap rows and columns in a much more chaotic and interesting way. Unlike normal Sudoku, we can ask, what if we have two rows (or columns) where candidates X are present in just two shapes. In that case, we can be certain that there will be two solutions (one for both boxes and both rows/columns) so any other candidate X in those shapes can simply go. (The doubling up theme is not new. Consider how
X-Wings are a doubled up version of Hidden Pairs).
