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Hockey Score Settlement (Posted on 2014-02-03) Difficulty: 3 of 5
Three teams A, B and C participated in a 3 sided hockey tournament. In three games, team A played team B, team B played against team C, and team A played against team C.
  1. The three final scores of the games consisted of the numbers 1, 2, 3, 4, 5, and 6.
  2. The difference between the team Aís higher score and the team B's higher score was one more than the difference between team Bís lower and team Cís lower score.
  3. The highest total of a teamís two scores was achieved by the team that lost the greatest number of games.
Which team achieved the highest total of its two scores?

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution Solution | Comment 1 of 2
The total of the scores is 21, so the highest total must be greater than 7. There were 3 games lost, so the greatest number of games lost by a team must be greater than 1. Therefore, by clue 3, a team lost 2 games and got a total score of at least 8. They could not have gotten 6 points in a game because they would have won that game. They could not have gotten 4 and 5 because they could not have lost both games. Therefore, they got 3 and 5. They lost the game with 5 points to a team that got 6 points. That leaves a team with 4 points to beat the 3 points. Their total score is 8. Since 8 is the highest total, no other team got 8 points. The team with 6 points could not have gotten 2 points because that would be 8 points. Therefore, they got 1 point. The team with 4 points got 2 points. Therefore, one team got 1 and 6 points, another team got 2 and 4 points, and another team got 3 and 5 points.

We know that the high scores of the teams are 4, 5, and 6. Therefore, the low scores are 1, 2, and 3. By clue 2, the difference between A's high score and B's high score must be 2, and the difference between B's low score and C's low score must be 1. That implies that A and B got 4 and 6 in some order. Therefore, C got 5. Since the team with 5 points also got 3 points, C got 3 points. Therefore, B's low score is 2 points. That means that B got 4 points, too. Therefore, A got 1 and 6 points.

Game 1:
A:1
B:2

Game 2:
A:6
C:5

Game 3:
B:4
C:3

Total:
A:7
B:6
C:8

C had the highest total.

Edited on February 3, 2014, 6:38 pm
  Posted by Math Man on 2014-02-03 10:46:37

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