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<TD class=title vAlign=baseline><NOBR>Grundy's
Game</NOBR></TD></TR>
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<P><A
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<P class=Text>A special case of <A class=Hyperlink
href="http://mathworld.wolfram.com/Nim.html">nim</A> played by the
following rules. Given a heap of size <IMG class=inlineformula
height=15 alt=n
src="Grundy's Game -- From MathWorld.files/inline1.gif" width=7
border=0>, two players alternately select a heap and divide it into
two unequal heaps. A player loses when he cannot make a legal move
because all heaps have size 1 or 2. Flammenkamp gives a table of the
extremal <A class=Hyperlink
href="http://mathworld.wolfram.com/Sprague-GrundyValue.html">Sprague-Grundy
values</A> for this game. The first few values of Grundy's game are
0, 0, 0, 1, 0, 2, 1, 0, 2, ... (Sloane's <A class=Hyperlink
href="http://www.research.att.com/~njas/sequences/A002188">A002188</A>).
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</P><SPAN class=crosslinkheader>REFERENCES:</SPAN>
<P class=Reference>Flammenkamp, A. "Sprague-Grundy Values of
Grundy's Game." <A class=Hyperlink
href="http://www.uni-bielefeld.de/~achim/grundy.html"><TT>http://www.uni-bielefeld.de/~achim/grundy.html</TT></A>.
</P>
<P class=Reference>Sloane, N. J. A. Sequence <A class=Hyperlink
href="http://www.research.att.com/~njas/sequences/A002188">A002188</A>/M0044
in "The On-Line Encyclopedia of Integer Sequences." </P>
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AS:</SPAN><BR>
<P class=citation>Eric W. Weisstein. "Grundy's Game." From <A
href="http://mathworld.wolfram.com/"><I>MathWorld</I></A>--A Wolfram
Web Resource. <A
href="http://mathworld.wolfram.com/GrundysGame.html">http://mathworld.wolfram.com/GrundysGame.html</A>
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<P class=copyright>© 1999 CRC Press LLC, © 1999-2006 <A
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