On the topic of simple chess variants played on a tiny board:

Mamikon's Mini-Chess is a game/puzzle played with just a white queen and black king on a 4x3 board, that is said to have eluded Kasparov.

https://web.archive.org/web/20140220104115/http://www.mamiko...

Mamikov Mnatsakanian is also the co-author with Tom Apostol of the wonderful New Horizons in Geometry. "As an undergraduate he specialized in the development of geometric methods for solving calculus problems by a visual approach that makes no use of formulas, which he later developed into his system of visual calculus."

https://www.amazon.com/Horizons-Geometry-Dolciani-Mathematic...

https://en.wikipedia.org/wiki/Visual_calculus

For fans of geometry I can recommend the following book:

Apostol, Mnatsakanian: New Horizons in Geometry : https://www.amazon.com/Horizons-Geometry-Dolciani-Mathematic...

See also: https://en.wikipedia.org/wiki/Visual_calculus