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"Twelve students of one class have held a rock-scissors-paper tournament. Each competed against each one exactly once. There were two points for a win, one point for a draw and no points for a defeat.

At the end of the tournament, all participants scored different scores. The player in second place has as many points as the last five together.

How did the game end between the players on the 7th and 9th place?"

Well I know how to find out how many points together can be in this game, and I even have a possible solution, but I have to include that a draw is possible, too.

Please give me a hint! ;)

Misha Lavrov
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Jana018
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    If you have a possible solution, please show it to us. – saulspatz Dec 27 '18 at 17:35
  • I don't know why but it's actually not possible to delete this post. I tried like a hundred times. – Jana018 Dec 27 '18 at 18:21
  • Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you. – saulspatz Dec 27 '18 at 18:27
  • Yes, that's right, that wouldn't be fair for him. But you just said that this question is lonely to be closed so I thought maybe I should delete it – Jana018 Dec 27 '18 at 18:29
  • No, that's not what I meant at all. I was just trying to help you attract attention to your question. Glad you got an answer. – saulspatz Dec 27 '18 at 18:32
  • Why have you deleted the description of the game from your question? – amd Dec 27 '18 at 22:00
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    It's a question of a running competition in another country! The participants could See this.... it has to be deleted!!!! – Jana018 Jan 01 '19 at 14:53
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    Editing out the question won't help if the answer is still there. Flag it for moderators with a link to the competition and they will do reasonable things. – Misha Lavrov Jan 01 '19 at 18:51

1 Answers1

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There were ${12\choose 2} = 66$ matches.

There are 2 points awarded in each match.

The bottom 5 played ${5\choose 2}$ matches among each other.

Even if they lose every match against every competitor not in the bottom 5, they score at least 20 points.

The second place finisher has at least 20 points

The first place finisher has at least 21 points.

No one scores more than 22 points

It is possible for the second place finisher to have 21 points and the first place finisher to score 22?

No, If the first place finisher scores 22 points, he won every match, including the one against the second place finisher.

The second place finisher scores 20 points The bottom 5 fail to sore a point off of anybody out of the bottom 5.

The 9th place finisher is in the bottom 5.

The 7th place finisher beat him.

Doug M
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    I just found out that this is a question of a competition in another country, so maybe you should delete your answer. I'm really thankful for your answer but I just wanted to know it for fun, others use it for this competition. – Jana018 Dec 27 '18 at 20:26
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    Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why) – Jana018 Dec 27 '18 at 21:13