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The books become like the first - Iran NMO 2006 - Problem6

Source:

September 23, 2010
inductionleast common multiplecombinatorics proposedcombinatorics

Problem Statement

Some books are placed on each other. Someone first, reverses the upper book. Then he reverses the 22 upper books. Then he reverses the 33 upper books and continues like this. After he reversed all the books, he starts this operation from the first. Prove that after finite number of movements, the books become exactly like their initial configuration.