# [2019.10.21] Why Semigroups are Harder than Sudoku

Cayley tables of semigroups are different from Sudoku in many ways,
although a Sudoku puzzle is just a partially filled Cayley table of
some quasigroup, another abstract mumbo-jumbo:

* although all possible semigroups from 9 items are enumerated, it's
 hard to find even an incomplete catalogue of them
* there are no readily available puzzles for semigroups. One need to
 construct them from scratch: analyze how many cells can be omitted
 for the completion to be unique
* Cayley tables of semigroups are associative, and there is no
 visible pattern of it. Associativity is a general case can only be
 proved with exhaustive checks. Any cell can be a spoiler, but one
 can't see which one with a naked eye

So, convolutional neural networks don't look like a feasible
candidate for the solution of associative tables filling-in problem.

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