## 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:

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.

Zuletzt geändert am 4. November 2022, 20:00 Uhr

Gelöst von apendleton, StefanSch, Jesper, Gryllulus, Krokant, Richard, SKORP17, Greg, Vebby, dhv, Mody, zuzanina, AstralSky, Julianl, lovely
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### Kommentare

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!

Zuletzt geändert am 4. November 2022, 19:56 Uhr

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.)

 Schwierigkeit: Bewertung: 86 % Gelöst: 15 mal Beobachtet: 2 mal ID: 000BVK

Lösungscode: