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<TITLE>Permutations: Treice</TITLE>
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<h1>Fixed-point-free permutations: "Treize" (thirteen)</h1>
      
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<td><p><b>A betting game: </b>
<br>Someone shuffles 13 playing cards
<br>and compares the shuffled sequence 
<br>with the original one.
<br>Your are winning, 
<br>if all the cards have moved the position...
<br>(de Montmori (1708),  N. Bernoulli (1713))
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Again a typical example of a permutation (the playing cards are permuted).
<br>Remember:
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The probability that at least one card lies on its old position is 63 % 
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nearly independent of the number of crads used ... 
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Analog: "Rencontre", using 52 playing cards: Leonhard Euler (1753),
<br>also: The problem of the interchanged hats, coats, bags, letters ...
<br>de Moivre (1718), Lambert (1771), Laplace (1812), 
...



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