Five teams, A, B, C, D, and E held the round-robin tournament to which every team plays a game against other teams 1 time respectively.
The number of victories of A and B is same and that of C and D is same, too.
The sum total of the number of victories of these four teams is six.
Supposing A won B and C, answer the team which C won.
Suppose that there was no draw.
The number of victories of A and B is same and that of C and D is same, too.
The sum total of the number of victories of these four teams is six.
Supposing A won B and C, answer the team which C won.
Suppose that there was no draw.
Answer
Since there is no draw and the number of victories of 4 teams of A~D is six, the number of victories of E is 10 - 6 = 4.
What was understood including A having won B and C is made into a table.
Supposing A also wins D, A is three victories, then since B lost to A, B is not three victories, it does not suit the conditions in the problem.
Therefore, it is found A lost to D and A is two wins and two losses.
Being rearranged up here, it is as shown in Table 2.
Since D is one win and C is three losses, if C lost to D, C comes to be four losses.
However it is not suit the conditions of the problem which state the number of victories of C and D are same, it turns out that C won D.
D
Solution
The number of games of this round-robin tournament is 5 × 4 / 2 =10 games.
Since there is no draw and the number of victories of 4 teams of A~D is six, the number of victories of E is 10 - 6 = 4.
What was understood including A having won B and C is made into a table.
Supposing A also wins D, A is three victories, then since B lost to A, B is not three victories, it does not suit the conditions in the problem.
Therefore, it is found A lost to D and A is two wins and two losses.
Moreover, since B is same as A, B is also two wins and two losses and B lost to A and E, it means that B win C and D.
Being rearranged up here, it is as shown in Table 2.
Since D is one win and C is three losses, if C lost to D, C comes to be four losses.
However it is not suit the conditions of the problem which state the number of victories of C and D are same, it turns out that C won D.
