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Monge's Shuffle


A shuffle in which cards from the top of the deck in the left hand are alternatively moved to the bottom and top of the deck in the right hand. If the deck is shuffled m times, the final position x_m and initial position x_0 of a card are related by

 2^(m+1)x_m=(4p+1)[2^(m-1)+(-1)^(m-1)(2^(m-2)+...+2+1)] 
 +(-1)^(m-1)2x_0+2^m+(-1)^(m-1)

for a deck of 2p cards (Kraitchik 1942).


See also

Cards, Shuffle

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References

Conway, J. H. and Guy, R. K. "Fractions Cycle into Decimals." In The Book of Numbers. New York: Springer-Verlag, pp. 157-163, 1996.Kraitchik, M. "Monge's Shuffle." §12.2.14 in Mathematical Recreations. New York: W. W. Norton, pp. 321-323, 1942.

Referenced on Wolfram|Alpha

Monge's Shuffle

Cite this as:

Weisstein, Eric W. "Monge's Shuffle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MongesShuffle.html

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