Mixing
Rock-Scissors-Paper-Tournament (Hard problem)
$begingroup$
"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! ;)
problem-solving
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
asked Dec 27 '18 at 17:22
Jana018Jana018
11
$endgroup$
|
show 3 more comments
$begingroup$
"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! ;)
problem-solving
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
asked Dec 27 '18 at 17:22
Jana018Jana018
11
$endgroup$
2
$begingroup$
If you have a possible solution, please show it to us.
$endgroup$
– saulspatz
Dec 27 '18 at 17:35
$begingroup$
I don't know why but it's actually not possible to delete this post. I tried like a hundred times.
$endgroup$
– Jana018
Dec 27 '18 at 18:21
$begingroup$
Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you.
$endgroup$
– saulspatz
Dec 27 '18 at 18:27
$begingroup$
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
$endgroup$
– Jana018
Dec 27 '18 at 18:29
$begingroup$
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.
$endgroup$
– saulspatz
Dec 27 '18 at 18:32
|
show 3 more comments
$begingroup$
"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! ;)
problem-solving
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
asked Dec 27 '18 at 17:22
Jana018Jana018
11
$endgroup$
"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! ;)
problem-solving
problem-solving
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
asked Dec 27 '18 at 17:22
Jana018Jana018
11
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
asked Dec 27 '18 at 17:22
Jana018Jana018
11
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
edited Jan 1 at 18:51
Misha Lavrov
44.3k555106
44.3k555106
asked Dec 27 '18 at 17:22
Jana018Jana018
11
asked Dec 27 '18 at 17:22
Jana018Jana018
11
asked Dec 27 '18 at 17:22
Jana018Jana018
11
11
2
$begingroup$
If you have a possible solution, please show it to us.
$endgroup$
– saulspatz
Dec 27 '18 at 17:35
$begingroup$
I don't know why but it's actually not possible to delete this post. I tried like a hundred times.
$endgroup$
– Jana018
Dec 27 '18 at 18:21
$begingroup$
Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you.
$endgroup$
– saulspatz
Dec 27 '18 at 18:27
$begingroup$
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
$endgroup$
– Jana018
Dec 27 '18 at 18:29
$begingroup$
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.
$endgroup$
– saulspatz
Dec 27 '18 at 18:32
|
show 3 more comments
2
$begingroup$
If you have a possible solution, please show it to us.
$endgroup$
– saulspatz
Dec 27 '18 at 17:35
$begingroup$
I don't know why but it's actually not possible to delete this post. I tried like a hundred times.
$endgroup$
– Jana018
Dec 27 '18 at 18:21
$begingroup$
Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you.
$endgroup$
– saulspatz
Dec 27 '18 at 18:27
$begingroup$
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
$endgroup$
– Jana018
Dec 27 '18 at 18:29
$begingroup$
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.
$endgroup$
– saulspatz
Dec 27 '18 at 18:32
2
2
$begingroup$
If you have a possible solution, please show it to us.
$endgroup$
– saulspatz
Dec 27 '18 at 17:35
$begingroup$
If you have a possible solution, please show it to us.
$endgroup$
– saulspatz
Dec 27 '18 at 17:35
$begingroup$
I don't know why but it's actually not possible to delete this post. I tried like a hundred times.
$endgroup$
– Jana018
Dec 27 '18 at 18:21
$begingroup$
I don't know why but it's actually not possible to delete this post. I tried like a hundred times.
$endgroup$
– Jana018
Dec 27 '18 at 18:21
$begingroup$
Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you.
$endgroup$
– saulspatz
Dec 27 '18 at 18:27
$begingroup$
Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you.
$endgroup$
– saulspatz
Dec 27 '18 at 18:27
$begingroup$
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
$endgroup$
– Jana018
Dec 27 '18 at 18:29
$begingroup$
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
$endgroup$
– Jana018
Dec 27 '18 at 18:29
$begingroup$
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.
$endgroup$
– saulspatz
Dec 27 '18 at 18:32
$begingroup$
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.
$endgroup$
– saulspatz
Dec 27 '18 at 18:32
|
show 3 more comments
1 Answer
1
active
oldest
votes
$begingroup$
There were ${12choose 2} = 66$ matches.
There are 2 points awarded in each match.
The bottom 5 played ${5choose 2}$ 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.
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
$endgroup$
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
There were ${12choose 2} = 66$ matches.
There are 2 points awarded in each match.
The bottom 5 played ${5choose 2}$ 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.
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
$endgroup$
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
add a comment |
$begingroup$
There were ${12choose 2} = 66$ matches.
There are 2 points awarded in each match.
The bottom 5 played ${5choose 2}$ 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.
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
$endgroup$
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
add a comment |
$begingroup$
There were ${12choose 2} = 66$ matches.
There are 2 points awarded in each match.
The bottom 5 played ${5choose 2}$ 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.
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
$endgroup$
There were ${12choose 2} = 66$ matches.
There are 2 points awarded in each match.
The bottom 5 played ${5choose 2}$ 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.
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
answered Dec 27 '18 at 17:49
Doug MDoug M
44.4k31854
44.4k31854
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
add a comment |
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
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.
$endgroup$
– Jana018
Dec 27 '18 at 20:26
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
$begingroup$
Really, Please delete this answer. I wanted to delete the question, too, but it doesn't work. (I don't know why)
$endgroup$
– Jana018
Dec 27 '18 at 21:13
add a comment |
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2
$begingroup$
If you have a possible solution, please show it to us.
$endgroup$
– saulspatz
Dec 27 '18 at 17:35
$begingroup$
I don't know why but it's actually not possible to delete this post. I tried like a hundred times.
$endgroup$
– Jana018
Dec 27 '18 at 18:21
$begingroup$
Why would you want to delete the post? That would also delete the answer that someone took the trouble to write for you.
$endgroup$
– saulspatz
Dec 27 '18 at 18:27
$begingroup$
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
$endgroup$
– Jana018
Dec 27 '18 at 18:29
$begingroup$
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.
$endgroup$
– saulspatz
Dec 27 '18 at 18:32