Chess players sometimes speak of “positional” moves. These moves do not have an immediate purpose such as attacking an opponent’s piece or getting one’s king out of check. Rather, they strengthen one’s overall position and create advantages and possibilities to exploit in the future. In other words, these positional moves are made on strategic grounds rather than on tactical ones. I’ve come to see that, particularly for ultra-difficult Sudokus, some numbers can similarly be placed on strategic grounds, in light of an overall appraisal of the “givens.”
This puzzle, Discrepancy, has the same basic design as several of the other Sudokus for which there are videos on this channel, including Platinum Blonde (#14), Golden Nugget (#15), Red Dwarf (#16), coly013 (#17), and tarx013 (#18). I began solving each of those puzzles by supplying a pair of numbers based on the givens. Then, at a certain point, I supplied a third number, similarly based on the givens, and this helped the solution take a crucial step forward.
For example, I began solving Golden Nugget by supplying a 2-4 pair; later I added a 7, and the need to avoid a rectangle consisting of 2-4, 4-7, and 2-7 pairs advanced the solution in the correct direction. Similarly, my approach to Red Dwarf starts with a supplied 7-8 pair; soon a 9 joins in, and a key move is to avoid a rectangle of 7-8, 8-9, and 7-9 pairs. Likewise, the solution to tarx013 starts with a supplied 4-8 pair; then a 5 is added, and it becomes vital to avoid a rectangle of 4-8, 4-5, and 5-8 pairs. Discrepancy, for its part, is a wonderfully complex and beautiful puzzle in that the solution involves avoiding two different rectangles of this type, one after another.
When I first made a video for Golden Nugget, I added the third supplied number by simply announcing, “Time to bring the 7s into play.” But I was a bit uncomfortable with that. I wanted to justify the 7, I can now see, on tactical grounds. So I made a follow-up video in which I did that, rather elaborately. However, my experience with Discrepancy has helped me see that I have basically been solving all of these ultra-difficult puzzles that depend on the same basic design by using strategically placed numbers-not tactically determined ones. I have been “reading” the givens and recognizing how the numbers will all need to relate to one another in order to form a solution. So now I can see that it is appropriate to supply numbers on a strategic basis, even if there is not an immediate tactical justification.
I certainly understand and respect those who will still want to fill in cells only on tactical grounds. But I believe we can all enjoy and appreciate Sudokus in our own ways. So when you get to 00:53 in this video and see a 4 appear-in purple, to indicate that I have supplied it-recognize that this has been done on strategic grounds. Just imagine me saying, “Time to bring the 4s into play.”
Update to information on video: Discrepancy was created by a Sudoku designer and theorist who went by the name of eleven on player forums.
5 сен 2024
