Problem

Source: IMO ShortList 1998, combinatorics theory problem 3

Tags: combinatorics, permutation, IMO Shortlist



Cards numbered 1 to 9 are arranged at random in a row. In a move, one may choose any block of consecutive cards whose numbers are in ascending or descending order, and switch the block around. For example, 9 1 6 5 3_ 2 7 4 8 may be changed to 91 3 5 6_ 2 7 4 8. Prove that in at most 12 moves, one can arrange the 9 cards so that their numbers are in ascending or descending order.


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