```From:           mverona@cs.umd.edu (Mary Verona)
Newsgroups:     rec.puzzles,sci.math
Subject:        Wythoff's game
Summary:        Need help for a three-dimensional extension of Wythoff's Game
Keywords:       Wythoff's Game, Wythoff's Nim, Wythoff pairs, Fibonacci sequences,
Date:           9 Jul 92 01:19:59 GMT
Organization:   U of Maryland, Dept. of Computer Science, Coll. Pk., MD 20742
```

```    I have a student who is working on a three-dimensional extension
of Wythoff's Game.  We would appreciate any help that may be available.

Two-dimensional Wythoff's Game is a combinatorial game played by
two players using two piles of objects.  On each turn, a player may remove
some or all of the objects from one pile or the same number of objects from
both piles.  The goal of the fame is for a player to remove all of the objects
on his or her turn.
The study of Wythoff's Game centers around the study of Wythoff's
pairs, which are positions in the Game where a player is guaranteed the
win if he or she has just moved to that position.  A Wythoff pair is an ordered pair (a,b) where a and b represent the number of objects in the respective
piles.  It turns out that the Wythoff pairs have several interesting
Fibonacci and golden ratio properties.
My student has attempted to move the game into three dimensions,
using three piles.  He hopes to find similar properties in the new
variation.  If you have any help or would like to see the Wythoff triples,