Barcelona 2002 Colloquium

--{ Barcelona 2002 }--

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Board Games in Academia V


Albert Violant i Holz

Peg Solitaire and Boole Algebras

The Peg Solitaire is a very well-known board game, that has its origins in the XVIII century. In a letter of Leibniz, dated in 1716, he says that "the play called solitaire make me feel pleasure in extreme". Its not surprising at all the amount of mathematics hidden in this board game. Its simplicity of rules and its versatility makes it suitable for a lot of investigations.

In my talk I will explain the close relationship between this play and Boole Algebras, that makes it appropriate to motivate this topic at university level. Every particular position of the pegs are associated to an element of a Boole Algebra, and every movement leaves this related element invariant. This will permit us, for example, to decide very easily which initial positions will never end with only one peg.


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