In a volleyball tournament the league match (round-robin matches) of 5 teams, A, B, C, D, and E is held.
There is one court and the schedule is for two days.
The game of this tournament is organized in accordance with the following administration rules.
<Rule 1>
In addition to two teams under game, there are one team that referee a game and two teams that are waiting to play a next game.
<Rule 2>
There are five games held a day.
<Rule 3>
One team does not hold two games continuously among one day. One team may hold the 5th game on Day1 and the first game on Day2.
<Rule 4>
Each team will referee a game one time with the 1st day on the 2nd, respectively.
A part of schedule organized according to this rule is presented as it is shown in the next table.
Fill in all blanks in the table for answer.
There is one court and the schedule is for two days.
The game of this tournament is organized in accordance with the following administration rules.
<Rule 1>
In addition to two teams under game, there are one team that referee a game and two teams that are waiting to play a next game.
<Rule 2>
There are five games held a day.
<Rule 3>
One team does not hold two games continuously among one day. One team may hold the 5th game on Day1 and the first game on Day2.
<Rule 4>
Each team will referee a game one time with the 1st day on the 2nd, respectively.
A part of schedule organized according to this rule is presented as it is shown in the next table.
Fill in all blanks in the table for answer.
Answer
Solution
The 3rd game on Day1 is A-D and since the waiting team of the 2nd game is also A and D, the 2nd game is B-E.
Since the waiting teams of the first game are B and E, the first game is C-D.
Since the 3rd game referee is a team other than A, C, D, and E, it is B.
The 4th game referee is D according to Rule 4.
Since the waiting teams of the 3rd game are C and E, the 4th game is C-E.
Since the waiting team of the 4th game is A and B, the 5th game is A-B.
The 2nd game on Day2 is A-E or D-E.
The 2nd game on Day2 is A-E or D-E.
If it would be A-E, since the waiting teams of the first game are also A and E, the first game will be C-D and will become the same as the first game on Day1.
Therefore, the 2nd game on Day2 should be D-E and a referee is A.
Since the waiting teams of the first game are D and E, the first game is A-C.
Since the 3rd game referee is D, the 4th game is A-E and a referee is C.
Finally, the 5th game turns out to be B-D.
