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Chatty Classmates (Posted on 2024-07-29)

Mrs Green is teaching a class of eight students, which she knows consists of four pairs of “Best Friends”. She needs to divide them into pairs for an activity, but she also knows that if she puts any pair of best friends together then they will chat all lesson and get no work done.

How many ways can she put them into productive pairs?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution (spoiler)

| Comment 1 of 3

The below is wrong. It ignores that a mismatch of a given student could be matched with either of the two members of any other pair.

What's sought is the number of derangements of 4 elements, a member of OEIS A000166, which includes a formula: round(n!/e).

When n=4, the number of derangements is round(n!/e) = round(8.82910658811462) = 9, which is the answer.

Edited on July 29, 2024, 11:09 am

Posted by Charlie on 2024-07-29 08:06:27

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