Counting Circles on a Loop
(Published on 17. October 2025, 18:48 by egubachu)
Rules
- Sudoku: Place the digits 1 to 9 once each in every row, column, and box.
- Loop: Draw a one-cell wide orthogonal loop through the grid, so that any two adjacent cells along the loop share an edge. The loop may not touch itself, not even diagonally.
- Counting Circles: Place some counting circles in the grid. Every two adjacent cells along the loop must contain exactly one counting circle, and the loop passes through all the counting circles.
- A digit on a counting circle indicates the number of counting circles containing that digit. Any digit on the loop that is not on a counting circle is the sum of the two adjacent digits along the loop.
- Pointing Arrows: A digit in a cell containing pointing arrows indicates the number of counting circles seen in the directions of all the arrows combined, not counting itself.
Click the image to play.
Thanks
A big thanks to Henry James for testing this puzzle!Solution code: Row 5
Comments
on 19. October 2025, 19:22 by Franktothejay
This was a brilliant puzzle full of really nice deductions. There were several moments when I felt really proud for figuring something out about it, which I feel is a sign of a well-constructed puzzle.
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Thank you so much Franktothejay! Your comment also makes me feel proud about setting the puzzle! Congratulations on your solve!
on 18. October 2025, 12:12 by Snookerfan
Fabulous puzzle! The rules looked absolutely ridiculous at first, but it worked so perfectly. The break-in was multi-layered and stunning in all layers. The whole solve was extremely satifsfying and fun. Thank you!
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Thank you so much Snookerfan! It makes my day that you enjoyed my puzzle so much!
I went through several formulations of the rules, and this formulation addressed all the concerns that came up through testing. Thanks so much for giving my puzzle a go, I always love having a snookerfan solve for my puzzles:)
on 18. October 2025, 01:41 by TrollErgoSum
Absolute joy, brutal break in but it flowed so smoothly after that and every digit felt well earned.
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Thank you so much for you comment, TrollErgoSum! Didn’t this breakin remind you of Braess’ Paradox? By allowing larger digits on the circles, the loop becomes shorter. Braess’ Paradox is the one where adding in a connector road, travel times become longer. It’s so counterintuitive:)
