[ttctciyf]

> Latin Squares are ‘n’x‘n’ grids containing exactly one of each of ‘n’ symbols in every horizontal row and vertical column [...]

> Although mathematicians have been unable to determine how many different 26x26 [Latin] Squares can be created, they have been able to determine that the number is at least 9.337 x 10^426, or approximately 2^1418

Seems surprising that the number hasn't been calculated exactly. I'd have guessed it's a mechanically solvable but tedious combinatorics problem, but obviously not.

[ddulaney]

It’s mechanically solvable but not in any practical timescale. A naive approach would be to check every square with no repeats in the rows, which requires (26!)^26 attempts, or roughly 5e691. Obviously you can improve that by exploiting symmetry, shifts, etc, but that only gets you a few orders of magnitude. There are much cleverer techniques, but when your baseline is so ludicrously impossible you need a real breakthrough to make any progress.