IMO Shortlist 2006 problem C5
Kvaliteta:
Avg: 0,0Težina:
Avg: 8,0 An
tournament is a contest with
players held in
rounds such that:
Each player plays in each round, and every two players meet at most once.
If player
meets player
in round
, player
meets player
in round
, and player
meets player
in round
, then player
meets player
in round
.
Determine all pairs
for which there exists an
tournament.
![(n, k) -](/media/m/9/e/d/9ed6c5a9b5c7d88b48645a4f3fbc6832.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![(i)](/media/m/2/b/9/2b900b6092ba26af1415020bbd427e84.png)
![(ii)](/media/m/a/6/5/a65ca45870cb4c928be31b9a8a6fc8e5.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![i](/media/m/3/2/d/32d270270062c6863fe475c6a99da9fc.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![i](/media/m/3/2/d/32d270270062c6863fe475c6a99da9fc.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![j](/media/m/7/9/e/79ebb10f98eb80d16b0c785d9d682a72.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![j](/media/m/7/9/e/79ebb10f98eb80d16b0c785d9d682a72.png)
Determine all pairs
![(n, k)](/media/m/e/e/8/ee8cc07da31f8abdf7ba15eb591c2d59.png)
![(n, k) -](/media/m/9/e/d/9ed6c5a9b5c7d88b48645a4f3fbc6832.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2006