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moves on a permutation of 1, 2, ..., 8

Source: 1991 Swedish Mathematical Competition p4

April 2, 2021
combinatoricspermutation

Problem Statement

x1,x2,...,x8x_1, x_2, ... , x_8 is a permutation of 1,2,...,81, 2, ..., 8. A move is to take x3x_3 or x8x_8 and place it at the start to from a new sequence. Show that by a sequence of moves we can always arrive at 1,2,...,81, 2, ..., 8.
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