1991 AHSME Problems/Problem 26

An $n$ -digit positive integer is cute if its $n$ digits are an arrangement of the set $\{1,2,...,n\}$ and its first $k$ digits form an integer that is divisible by $k$ , for $k = 1,2,...,n$ . For example, $321$ is a cute $3$ -digit integer because $1$ divides $3$ , $2$ divides $32$ , and $3$ divides $321$ . Howmany cute $6$ -digit integers are there? The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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1991 AHSME Problems/Problem 26