Problem 54390. That's not my hat!

There exists a highly secretive hat consortium. Members possess identical hats. The members are invited to a meeting. All of them bring their hats, but are required to leave them in the shared cloakroom. During the meeting an earthquake strikes the region, leaving the cloakroom a mess. When the members return to the cloakroom, they find all the hats lying on the floor, rendering it impossible to determine the owners. Unwilling to dwell on this, the members each pick up a random hat and leave. Given the number of attendees n>0, the function c computes the number of distinct events where none of the members pick up their original hat. Your task is to define this function.
Solve

Solution Stats

92.86% Correct | 7.14% Incorrect
Last Solution submitted on Nov 14, 2025

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combinatorics recursion

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