49. kz0: A small change in the numbers may require a big change in the solving

On the Enjoy Sudoku forum, a search has been ongoing since the early years of Sudoku for the most difficult puzzles that can be created or discovered.* (It was in the thread for that search that I found many of the Sudokus for which there are videos on this channel.) Recently one approach that has proved fruitful has been to start with known ultra-difficult puzzles, make various changes to them, and see whether that yields further ultra-difficult puzzles. It seems to me that this be might how kz0 was created, although I don’t know for sure. It is very similar to Champagne dry, but with a small but significant change that makes it a great challenge of its own. In video #47, I explain how I looked at the starting numbers of Champagne dry and concluded that it was intuitively reasonable that the path to the solution should involve the 5s and 9s constraining each other, and that the cells in columns 2 and 3 of row 6 seemed like a promising place for that to happen. Putting those numbers in those cells created a further constraint throughout column 3 that in fact led to a solution. Interestingly, it turns out that in kz0 those same two cells also contain a 5 and a 9—but in the reverse order. So it seems that having those numbers there may indeed have been intrinsic to the structure of Champagne dry and that reversing them may have been a first step in creating kz0. Perhaps. This change shakes things up throughout the grid so that, while it is still recognizably similar to Champagne dry (compare, for example, the upper right block of both puzzles, where the 6 and 7 just switch places), a different approach must be taken to find the solution. Both a forcing chain (01:07) and an “extended unique rectangle”** (01:44) are needed. The solution to kz0 also involves determining what two numbers to put in the top two cells in column 3 (00:24); some of the possibilities falsify quickly, but others (unlike in Champagne dry) require more than a few steps to assess. So one might conclude that, based on the methods required to solve it, kz0 might be even more of a challenge than Champagne dry. In any event, the apple certainly doesn’t fall far from the tree. Chapters: 00:00 Reading the givens 00:24 Finding two key numbers 01:07 Help from a forcing chain 01:44 An extended unique rectangle *forum.enjoysudoku.com/the-hardest-sudokus-new-thre… **www.sudokuwiki.org/Extended_Unique_Rectangles