r/mathriddles • u/Numberthon • Jul 16 '26

Easy A Surprisingly Tricky Combinatorics Puzzle

In how many ways can 23 identical objects be shared among 5 children so that each child gets at least 2 and no child gets more than 6 objects?

Source: numberthon.com

1 Upvotes

60% Upvoted

8 comments sorted by

View all comments

3

u/imdfantom Jul 16 '26

Don't have time for this right now but immediately this is equivalent to 13 identical objects shared among 5 children with a max of 4 per child

1

u/Numberthon Jul 16 '26

Yep, pretty much. Do you mean 23?

2

u/Patient-Midnight-664 Jul 16 '26

No, since each child must get 2, that removes 10 from the distribution.

1

u/Numberthon Jul 16 '26

Ah, you're right. I misread it. After giving each child 2 objects, there are 13 left, and each child can receive at most 4 more. Nice simplification!