perplexus.info :: Just Math : Chatty Classmates

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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

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

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info