MathDB
Number of operations not greater than (2n/k)².

Source: Baltic Way 2005/6

November 7, 2005
combinatorics proposedcombinatorics

Problem Statement

Let NN and KK be positive integers satisfying 1KN1 \leq K \leq N. A deck of NN different playing cards is shuffled by repeating the operation of reversing the order of KK topmost cards and moving these to the bottom of the deck. Prove that the deck will be back in its initial order after a number of operations not greater than (2N/K)2(2N/K)^2.