Digital Loop
(Published on 22. May 2025, 22:44 by mathpesto)
Rules:
Loop: The grid contains an orthogonal loop which must not touch itself orthogonally but may touch itself diagonally. Cells on the loop contain the digits 1–9 and among these cells, digits cannot repeat in the grid's rows nor columns.
Fillomino: Divide the remaining cells in the grid into polyominoes so that no two polyominoes of the same size share an edge. Each fillomino cell contains a number equal to the size of its polyomino.
Arrows: If an arrow is in a cell on the loop, the cell contains a number equal to the sum of all fillomino cells in that direction. If an arrow is in a fillomino cell, the cell contains a number equal to the sum of all cells on the loop in that direction. (Note: A fillomino cell can contain a number greater than 9.)
Solve online:
Solution code: Digits on the loop in Column 9 (top to bottom)
Comments
on 29. May 2025, 22:20 by Christounet
Classic mathpesto puzzle! Very enjoyable. Thanks :)
on 29. May 2025, 08:16 by Nordy
Insane. Many absolutely gorgeous steps from start to finish. Once I figured out a solid notation strategy, it was remarkably smooth!
on 28. May 2025, 17:48 by skuntsel
What an stunning puzzle! It was an absolute treat to solve! The quality is just impeccable, every next step is truly rewarding with several breakthroughs along the way that feel really nice! True, it’s hard to keep track of arrows, especially on a phone, with a loop rendered, but that’s a minor thing. Really fascinating how it all resolves, and how much weight there is on any arrow. And you expect it to crumble after two, no three break-ins, but it resists just until the end leaving ambiguity along the way. Just a perfectly blended and uniformly unfolding setting. Liked every minute solving it, it surely is one of the best puzzles of the year. Of course nobody expected anything less from you, Math, but it is this uncanny feeling you often get that some minds are by miles ahead of many. Thank you for sharing this amazing construction!
on 26. May 2025, 22:09 by teff
always a pleasure Math!
on 23. May 2025, 20:55 by twobear
Enjoyed solving it immensely. Thank you!!
on 23. May 2025, 14:54 by Snookerfan
Great puzzle! Fascinating ruleset. I got a little lost in keeping track of all the arrows, so it took me quite a while, but I had fun all the way. Thank you
on 22. May 2025, 23:12 by shartus
I was able to place a 2 in r8c12
