Mathemagics
(Published on 2. April 2026, 03:01 by Lithium-Ion)
This puzzle has been my fourth feature on Cracking the Cryptic (click here to see Mark solving it). It is a loop-based empty grid puzzle with a quite unique ruleset. I hope that you enjoy the puzzle. Constructive feedback is always appreciated! The rules are as follows:
Normal Sudoku rules apply. Draw a one-cell wide loop that moves orthogonally through the center of cells and does not branch, intersect with itself or touch itself (neither orthogonally nor diagonally). The loop has to visit each box at least once. For each box, the maximum number of cells belonging to the loop is k, where k is the box number. Within each box, the box number has to be part of the loop. Boxes are numbered in normal reading order. Two orthogonally adjacent cells are only allowed to contain digits that sum to 7 or 10 if both cells are not part of the loop. The 24 cells that are enclosed by the loop have to contain two magic squares. A magic square is a 3x3 region containing the digits from 1 to 9 once each, where each row, column and diagonal must sum to the same value.
Important note: Due to some helpful comments under the CtC video, I realized that the wording of the "sum to 7 or 10 rule" should read more precisely: Two orthogonally adjacent digits are neither allowed to sum to 7 nor to 10 if at least one of those two cells is part of the loop.
You can play this puzzle via the following link: https://sudokupad.app/a8nfw8uk8j
Normal Sudoku rules apply. Draw a one-cell wide loop that moves orthogonally through the center of cells and does not branch, intersect with itself or touch itself (neither orthogonally nor diagonally). The loop has to visit each box at least once. For each box, the maximum number of cells belonging to the loop is k, where k is the box number. Within each box, the box number has to be part of the loop. Boxes are numbered in normal reading order. Two orthogonally adjacent cells are only allowed to contain digits that sum to 7 or 10 if both cells are not part of the loop. The 24 cells that are enclosed by the loop have to contain two magic squares. A magic square is a 3x3 region containing the digits from 1 to 9 once each, where each row, column and diagonal must sum to the same value.
Important note: Due to some helpful comments under the CtC video, I realized that the wording of the "sum to 7 or 10 rule" should read more precisely: Two orthogonally adjacent digits are neither allowed to sum to 7 nor to 10 if at least one of those two cells is part of the loop.
You can play this puzzle via the following link: https://sudokupad.app/a8nfw8uk8j
Solution code: Digits in row 1, read from left to right.
Solved by ZornsLemon, zeniko, marcmees, lrbhandanshi, BuffADC, DigitCounter, lm_12, JohnMoore, stephan_71, SKORP17, vi92, puzzle_hunter, ax_86, 6rank, apothycus, Exigus, Ftown778, agenthans, HonkIfYouLoveBeer, taj
Comments
on 2. April 2026, 09:04 by zeniko
I like how the loop tightens around the two squares and how you found a not too convoluted way to disambiguate towards the end. Thanks for sharing and congrats on the feature.
