Greater than Consecutive Sudoku - 11 Pairs
(Eingestellt am 3. November 2022, 06:35 Uhr von Nylimb)
Standard sudoku rules apply: Fill the grid with digits from 1 to 9, so that every row, column, and 3x3 box contains each digit exactly once. An inequality sign between 2 orthogonally adjacent cells means that the digits in those cells differ by 1, and the direction of the sign shows which digit is larger; e.g. if a 6 is to the left of a 7, the sign would be "<". All possible inequality signs are given.
In 2012 I made a puzzle with this rule, which I called Consecudoku, and used it for a geocache: Solving the puzzle would give the solver the GPS coordinates to find a hidden container somewhere.
My original puzzle had 29 pairs of adjacent and consecutive digits. About a year ago I wondered how few pairs such a puzzle could have, and still have a unique solution. After several reductions, I found the one shown here, with 11 pairs. I doubt that that's minimal, but I ran out of ideas for improving it. (P.S.: Thanks to qiuyanzhe, who mentioned, in a comment below, that an 8-pair puzzle exists, and later found a 5-pair puzzle! I've confirmed those by a computer program, but I think solving them by hand is unlikely.)
Recently I discovered that 2 puzzles with the same rule had been published here by Richard:
24 Ways to survive a Dutch Advent (18): Greater than Consecutive Sudoku
Sudoku Variants Series (074) - Greater than Consecutive
Those reminded me that I hadn't published this one yet, so now I have. For consistency with Richard's puzzles, I've changed the puzzle name and used inequality signs instead of the arrows that I used before.
You can solve this in Penpa or the CTC app.
Lösungscode: Row 9 and column 1.
Kommentare
am 19. Februar 2024, 07:42 Uhr von thorscouts
Enjoying working my way through these puzzles. Daughter jumped in today while we were visiting her at college and tried one that we did earlier. She loved it as well. She'd never tried a sudoku that had no numbers to start with and that you needed to make other deductions to get the solution. We are really enjoying these!
am 6. Juli 2023, 12:41 Uhr von Prof.Dori
It is a shame that this puzzle hasn't higher rating considering it has a logical solution entire time.
am 13. November 2022, 06:11 Uhr von Richard
Don't be intimidated by so few clues! This puzzle is very fun and solving it can add new logic to your tool kit! It certainly deserves a rating and red stars! Highly recommended! Give it a go...
am 4. November 2022, 20:00 Uhr von Nylimb
Updated comment about qiuyanzhe's puzzles.
am 4. November 2022, 06:05 Uhr von Nylimb
Added comment about the 8-pair puzzle mentioned by qiuyanzhe.
am 3. November 2022, 20:28 Uhr von Richard
Thx for this very fun little puzzle! Well done setting with so few clues!
am 3. November 2022, 13:47 Uhr von qiuyanzhe
One may try as if standard Consecutive sudoku. I remembered a path with 1-9 at r3c3-r3c5-r7c5-r7c7 makes a unique solution, but not checked now. There must be puzzles with fewer clues (very likely to be non-logical.)
@qiuyanzhe: Interesting! I've confirmed this by using a computer program which does a lot of bifurcation, but I haven't figured out a way to solve it without that. Anyway, that shows that a puzzle with just 8 pairs exists.
qiuyanzhe:(edit 22Nov04 07:30)Found a puzzle with 5 pairs: r5c4<r5c5<r6c5<r6c6,r4c4<r4c3<r4c2.
btw no logical path found, not recommended to try puzzles in this comment.
@qiuyanzhe: Amazing! I never expected a 5-pair puzzle to be possible. My program took almost 4 hours to confirm that the solution is unique. (It's written in python, and designed to be general, not fast.)
