Cylic Modular Casscade
(Published on 22. September 2022, 09:06 by glenfletcher)
- Unless explicitly stated, rules apply to the toroid grid formed by allowing the provided grid to wrap around both horizontally and vertically.
- Digits must not repeat in a region.
- Digits must form the same 9-cycle across each row.
- For every 4-length subsequence of the 9-cycle across each row, the sum of the first and last digits must be congruent modulo 9 with the sum of the middle two digits. (i.e. R1C9 + R1C3 ≡ R1C1 + R1C2 (mod 9)).
- The sum of the differences between all unique pairs in the 9-cycle across each row must be minimised, subject to the other rules. (i.e. |R1C9 – R1C1| + |R1C1 – R1C2| + … + |R1C8 – R1C9| must be minimized).
- Digits must form the same 9-cycle down each column.
- Digits must form the same 9-cycle up each positive diagonal.
- Digits must not be congruent modulo 3 with digits orthogonal adjacent or adjacent along any positive diagonal. (i.e. the following must all be false, R3C4 ≡ R2C4 (mod 3), R3C4 ≡ R4C4 (mod 3), R3C4 ≡ R3C3 (mod 3), R3C4 ≡ R3C5 (mod 3), R3C4 ≡ R2C5 (mod 3) and R3C4 ≡ R4C3 (mod 3)).
- Digits must form a recurring 3-cycle composed of those digits congruent modulo 3 along negative diagonals, and the cycle must be the same cycle for each group of digits that are congruent modulo 3. (i.e. R1C4 ≡ R2C5 ≡ R3C6 (mod 3) but R1C4 ≠ R2C5 ≠ R3C6 ≠ R4C7 = R1C4).
- The values (A and B) indicated down the left-hand side of the grid are the sum of digits between the two extreme digits (1 and 9). These sums apply to the provided unwrapped grid (i.e. if R1C3 was 9 and R1C4 was 1, the sum for row 1 would be 0, not 2 + 3 + … + 8). These values have a difference of 5.
Open on F-Puzzles
Open on Cracking the Cryptic
Cyclic permutation
Modular arithmetic
Solution code: First 2 rows
Last changed on on 31. October 2022, 01:30
Solved by ugly2333
Comments
on 31. October 2022, 01:30 by glenfletcher
Rewrote rules and included examples to try and make the rules clearer, added solutions to the CTC app, Increased difficulty rating (based on the public rating of Diophantine Addict, which I consider to be of equivalent difficulty)
