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Cards numbered 1-1000 are to be placed on a ×1×1994 rectangular board

Source: All Russian MO 1994 ARO

July 29, 2018
combinatoricsboard

Problem Statement

Cards numbered with numbers 11 to 10001000 are to be placed on the cells of a 1×19941\times 1994 rectangular board one by one, according to the following rule: If the cell next to the cell containing the card nn is free, then the card n+1n+1 must be put on it. Prove that the number of possible arrangements is not more than half a mllion.
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