# The original proof of Wythoff's game

I am looking for the original proof of Wythoff's game. Wythoff provided the first full analysis of this game in "A modication of the game of nim, Nieuw Archief door Wiskunde, 199{202, 1907". However, I don't have access to the paper and I am also afraid that it is written in Dutch. Does anyone know any paper or book in which I can find his proof in Enlgish?

The Wythoff game is played by two persons. Two piles of counters are placed on a table, the number of each pile being arbitrary, say $(i,j)$. The players play alternately and either take from one of the piles an arbitrary number of counters or from both piles an equal number. The player who takes up the last counter or counters, wins.

The cold position of Wythoff game is given by $([n \phi],[n \phi^2])$ for $n \in \mathbb{N}$, where $\phi$ is the golden ratio and $[x]$ denotes the integer part of $x$.

• If the title is in English, that's a good sign that the paper is in English. – bof Dec 25 '13 at 18:34
• archive.org/stream/nieuwarchiefvoo03genogoog#page/n9/mode/2up – Myself Dec 25 '13 at 20:35
• Wow thank you for the link. How do you find the archive? I occasionally have trouble finding old papers and would like to know a good way to find them. – WythoffGame Dec 26 '13 at 0:47
• I used ... Google :-) Maybe it helps that I knew the actual name to be "nieuw archief Voor wiskunde" (with a V). – Myself Dec 27 '13 at 10:03