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 voor Wiskunde, pp. 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 counters on 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 $(\lfloor n \phi \rfloor, \lfloor n \phi^2\rfloor)$ for $n \in \mathbb{N}$, where $\phi$ is the golden ratio and $\lfloor x\rfloor$ denotes the integer part of $x$.

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    $\begingroup$ If the title is in English, that's a good sign that the paper is in English. $\endgroup$
    – bof
    Dec 25, 2013 at 18:34
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    $\begingroup$ archive.org/stream/nieuwarchiefvoo03genogoog#page/n9/mode/2up $\endgroup$
    – Myself
    Dec 25, 2013 at 20:35
  • $\begingroup$ 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. $\endgroup$ Dec 26, 2013 at 0:47
  • $\begingroup$ I used ... Google :-) Maybe it helps that I knew the actual name to be "nieuw archief Voor wiskunde" (with a V). $\endgroup$
    – Myself
    Dec 27, 2013 at 10:03

1 Answer 1


Excellent, Myself! Link to the first page and to the review.


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