Friday, 30 August 2013

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
One square diagonally
Two squares horizontally / vertically
Knight move
Two squares diagonally
Three squares horizontally / vertically
Four squares horizontally / vertically
Three squares diagonally
Five squares horizontally / vertically
Four squares diagonally
Six squares horizontally / vertically
Seven squares horizontally / vertically
Five squares diagonally
Six squares diagonally
Seven squares diagonally

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!

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