Logic Masters Deutschland e.V.

Some Octopus

This is somedoku #8. Check out the rest of the puzzles in the somedoku series.

When ThePedallingPianist discovered we were both working on an Octopus Somedoku puzzle he suggested we collaborate. This puzzle is the result of that collaboration, and it is a puzzle we are both quite proud of!

I felt that this puzzle should have ended up on his LMD page, both because I wanted him to have a somedoku published and because he did the lion’s share of the work with this construction. But he knew that secretly I wanted an octopus puzzle to post on my page; so he did the only thing he could do… he made his own puzzle. Now we both have a somedoku octopus puzzle to share!

Our gratitude to Marty Sears for letting us use his background image and for inventing the counting circle rule that features prominently in both puzzles. We are also grateful to the members of the community who see a ruleset like this and dive in, trusting that we have cooked up something fun for you. We hope you enjoy solving it as much as we enjoyed setting it!

Rules:

Somedoku: Fill each cell with a digit from 1-9. For every row 'n' and column 'n' there are exactly 'n' different digits. The remaining cells are filled with repeats.

Octopus: Draw 8 tentacles, all the same length (in number of cells) that emanate from the head (R5C5) and reach the edge of the grid, where they stop immediately. Tentacles do not cross or overlap, except at the head. Opposite tentacles are considered as single lines, which have 180-degree rotational symmetry.

Counting Octopus: A digit on the octopus shows how many times that digit appears on the octopus.

Counting Anti-Octopus: A digit that never appears on an octopus shows how many times that digit appears in the puzzle.

Crabs: Help feed the octopus by catching every crab with one of the tentacles (i.e. all crabs lie on the octopus), and no two crabs contain the same digit.

The Octopus’ four lines are:

• Dutch Whisper: Adjacent digits differ by at least 4.
• Entropic: A digit does not appear within two steps of another from the same entropic set ({1,2,3}, {4,5,6}, and {7,8,9}).
• Modular: A digit does not appear within two steps of another from the same modulo set ({1,4,7}, {2,5,8}, and {3,6,9}).
• Palindrome: The line reads the same forwards as backwards.

Local Constraints: an inequality sign points to a smaller digit; digits separated by a white dot are consecutive; digits separated by a black dot are in a 1:2 ratio; and digits separated by an X sum to 10.

We hope you enjoy it, if you do please leave a rating and a comment below!