Amphisbaena
(Published on 14. November 2025, 16:00 by TripleABattery)
This puzzle was inspired by Jreg's puzzle “The Basilisk”. Thanks to all the testers on the CtC discord for their help, especially Jeremy. I hope you enjoy!
Sudoku: Place the digits 1-9 into every row, column, and 3×3 box.
Serpent: Draw a serpent in the grid. The serpent is a single unbranching line starting in one of the 3×3 boxes and passing through each box exactly once before stopping in the final box; the exact order in which the serpent visits these boxes is to be determined by the solver. The serpent only moves orthogonally (left, right, up, down) and cannot visit a single cell multiple times.
The boxes are numbered in a standard reading order. In each box number N, the serpent occupies exactly N cells. Those cells contain a consecutive set of digits 1 through N in any order. E.g.: In the middle row of boxes, the leftmost box is number 4. The serpent occupies 4 cells in this box and they contain the digits 1-4.
Along the serpent, adjacent digits differ by at most 4.
Digits on corners of the serpent cannot repeat on the diagonal the corner "points to". E.g.: if the serpent travels from r5c4 to r4c4 to r4c5 and r4c4 contains a 3, then r1c1, r2c2 and r3c3 cannot contain a 3.
Circles: Digits in circles count the number of serpent cells in their surrounding 3x3 square, where they also cannot repeat. Digits in circles also count the number of corners of the serpent seen in its row and column combined, not including itself.
Dots: Digits separated by a white dot are consecutive.
I'm particularly happy with this construction, because my favourite number happens to appear twice in the grid (read horizontally). Extra credit to anyone who can tell me what that is in the comments. Here's a hint to start, it's a 3-digit prime number.
Solution code: Digits in row 1 (left to right).
