Bishops Problem

Author

Eric W. Weisstein
December 28, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Games/BishopsProblem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BishopsProblem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Chess`;

Maximum number of bishops

Counts

Table[BishopsDistinct[n],{n,20}]

Display

Show[Graphics[ChessPieces[StringReplace["\<
v       
v      v
v      v
v      v
v      v
v      v
v      v
v","\n"->""],
OutputFormat->"Display"],AspectRatio->Automatic,PlotRange->{{-4,4},{-4,4}}]]

Export as EPS

Show[Graphics[ChessPieces[StringReplace["\<
v       
v      v
v      v
v      v
v      v
v      v
v      v
v","\n"->""],OutputFormat->"EPS"],AspectRatio->Automatic,PlotRange->{{-4,4},{-4,4}}]]

Rotationally and reflectively dinstint

Dudeney

?Even

B[n_?EvenQ]:=2^((n-4)/2)(2^((n-2)/2)+1)
B[n_?OddQ]:=2^((n-3)/2)(2^((n-3)/2)+1)

Table[B[n],{n,10}]

Equivalent

B2[n_]:=2^(n-3)+2^(Floor[(n-1)/2]-1)

Table[B2[n],{n,10}]

Minumum number of bishops

pieces=StringJoin@Table["   v    ",{8}];

Display

Show[Graphics[ChessPieces[pieces,OutputFormat->"Display"],AspectRatio->Automatic,PlotRange->{{-4,4},{-4,4}}]]

Export as EPS

Show[Graphics[ChessPieces[pieces,OutputFormat->"EPS"],AspectRatio->Automatic,PlotRange->{{-4,4},{-4,4}}]]