- #1

tellmesomething

- 269

- 27

- TL;DR Summary
- A combinatorics problem solved in a needless and agonizing way. Found clever alternate solutions but do not understand why and how it works.

Right, so i came across this problem

Smart approach: I found this

Thankyou.

My approach was uninteresting and not clever at all. I started making cases i had to make about 14 of them and while it didnt take long,i think it would have been very tedious for a bigger number say 16 players. But it was logical and i got my answer.Eight runners wearing their favorite colored jerseys have just completed a 100m race and we know the following results.

The BLUE runner finished AHEAD of the TEAL runner The PINK runner finished AHEAD of the GREEN runner The PURPLE runner finished AHEAD of the ORANGE runner

The GREY runner finished AHEAD of the RED runner.

How many different ways can the eight runners finish the race?

Smart approach: I found this

Can someone please explain whats happening here? I understand that 8! is the total number of ways to arrange the players if there were no restriction, but the dividing by 2^4 i do not get.Each restriction divides the total number of permutations by 2. Since they are symmetric and independet, you have 8!/(2^4).

Thankyou.

Last edited by a moderator: