Note: Sudoku Set Equivalence Theory: The Phistomefel Ring

Nov 25, 2022

During the pandemic I became a fan of Cracking the Cryptic, a Youtube Channel in which two English guys solve — often very challenging — variant sudoku puzzles. It turns out these puzzles often have fascinating and clever emergent logic puzzles embedded within them.

One great example, is the Phistomafel Ring, which is a surprising property that all sudoku puzzles have!

It states that:

The 2x2 corner blocks of any Regular 9x9 Sudoku Grid contain exactly the same digits as the cells that border the edge of box 5 (including the corners).

It turns out one can relatively easily deduce this using set equivalence theory, and there have been a number of Sudoku puzzles which set you up to discover this property and then require you to use it to solve the puzzle!

For a detailed and illustrated explanation, see: https://crackingthecryptic.fandom.com/wiki/Phistomefel_Ring

A nicely illustrated example can be found in this video from the Youtube channel Numberphile where guest Simon Anthony of Cracking the Cryptic walks us through an approachable description: