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 times, the final position and initial position of a card are related by

for a deck of cards (Kraitchik 1942).

**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.

© 1996-9

1999-05-26