The most geometrically awesome chess problem

"All conceptions in the game of chess have a geometrical basis."

- Eugene Znosko-Borovsky

by Junta

 

At the end of a lecture I gave at the universities' training camp in Niigata earlier this month, I showed a problem I first saw a few years ago.

Composed by Unto Heitonen

Published in Die Schwalbe, 2000

White to play - White's king is on h8, not a1

This is not a regular chess problem, but one in the realms of fairy chess, i.e. unorthodox problems not involving direct mates. The variant used here is the 'double maximummer', where White and Black must each play the geometrically longest move possible on the board on every turn.

We will consider each square to have dimensions of 1x1 units, and the distance between one square and the square horizontally or vertically adjacent to it 1 unit. The distance to a diagonally adjacent square would be √2, or approximately 1.4 units.

The list of relevant distances is below, rounded to one decimal place.

One square horizontally / vertically	1
One square diagonally	1.4
Two squares horizontally / vertically	2
Knight move	2.2
Two squares diagonally	2.8
Three squares horizontally / vertically	3
Four squares horizontally / vertically	4
Three squares diagonally	4.2
Five squares horizontally / vertically	5
Four squares diagonally	5.7
Six squares horizontally / vertically	6
Seven squares horizontally / vertically	7
Five squares diagonally	7.1
Six squares diagonally	8.5
Seven squares diagonally	9.9

So the first move for White would be 1.Bf1-d3, longer at 2.8 units than a knight move (2.2) or a rook move of two squares (2). Black moves after White like in normal chess, and after some time (it won't be a walk in the park!) the game will end in a certain way. Progress is slow at the start.

Note: If one side is checked, they must escape the check with, of course, the longest move possible.

I have no idea how composers create pieces of work like these, but please try this out over the board, not on the computer screen - be careful not to overlook making a mistake, or you'll have to start all over again. Enjoy!