Puzzling Asked by tazboy on June 23, 2021
I keep getting stuck on the NY Times Sudoku medium difficulty puzzles. I go through one number at a time and narrow down large box where that number can only be in two spaces. When I finish the nines I start back at the ones using the information from what numbers were determined in the first step. Then I go to the rows and columns and find ones that have around three or less boxes left, then I fill those candidates in. Then I’m stuck. Any thoughts on what strategy I’m not understanding or what things I could look for?
Stiv's answer is right (+1), but let me share another technique which might help you discover this in the future.
Correct answer by Glorfindel on June 23, 2021
Sometimes you have to look at rows and columns which have more than 3 empty spaces left! Consider the space on the third row between the 6 and 2...
Your strategy should work for most sudokus if you don't limit yourself in this arbitrary way. Consider ALL rows and ALL columns, even if they have 4 or more empty squares, and you should find places you can make progress, like in my example above. Good luck!
Answered by Stiv on June 23, 2021
Spoiling all the candidates in the attached image, but useful tool that can help you with hints, and the strategy behind the hint: https://www.sudoku-solutions.com/index.php?page=sudoku9by9
I think it usually gives you the easiest hints first, and then more and more complex strategies as needed.
Answered by Viktor Mellgren on June 23, 2021
When you find rows and columns that have only three boxes left you fill those numbers in (green in the image). Switch contexts and realize you now have only three empty boxes in the top-right square.
Answered by Jason Goemaat on June 23, 2021
Sometimes you need to look not only to separate numbers, rows and columns, but also the whole rows and columns of 3x3 blocks. In your example, you can notice that in top right 3x3 square, number 7 can be only in the top row. This cancels the possibility of number 7 being in the first row in the left block, leaving the number 9 the only option in the top left corner.
Answered by Jakuje on June 23, 2021
Starting with the givens in the original puzzle (not taking your eliminations into account) and after propagating the obvious constraints from the givens, the puzzle is solved with:
a hidden-single-in-a-column (==> r3c1 = 8),
followed by two interactions between rows and blocks (the most elementary rules after singles):
5 in row r9 ==> r7c2 ≠ 5
6 in row r5 ==> r4c8 ≠ 6, r4c7 ≠ 6
Answered by Denis Berthier on June 23, 2021
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