Answer 1. There will be 15 matches when 6 people play in the tournament.

1v2, 1v3, 1v4, 1v5, 1v6. This is 5 games 2v3, 2v4, 2v5, 2v6. This is 4 games 3v4, 3v5, 3v6. This is 3 games 4v5, 4v6. This is 2 games 5v6. This is 1 game.

5 + 4 + 3 + 2 + 1 = 15 games altogether. For 6 players, only 3 games can be played each half hour so the tournament will take 2.5 hours

2. Repeating the pattern above for 15 people there will be: 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 mathches

3. Complete this table for a similar type of tournament for the numbers of players given.

Number of players

Number of matches

2

1

3

3

4

6

5

10

6

15

15

105

100

4950

n

0.5(n^{2} − n)

4.105 games will take 105/4 hours = 26.25 half hours i.e. The tournament will last 13.5 hours

5. If there are 8 tables, the tournament will take 105/8 half hours = 13.125 half hours i.e. The tournament will last 7 hours.