3
$\begingroup$

There are 12 people. These people start in 4 groups - each with 3 people. They swap groups 4 times, so they are in a total of 5 groups. Is it possible for each person to be in a group with every other person at least once?

$\endgroup$
4
$\begingroup$

The answer is

No

Reasoning

If each person has only been in 5 groups, they've only been in a group with at most 10 people (out of 11 others).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.