ReasoningAges 10-12

Round-robin & network connections

Use n(n − 1) ÷ 2 to count the total number of unique pairwise connections or games in a group. Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Round-robin & network connections

Take your time. Show your thinking.

1. In a round-robin tournament with 6 players, every player plays every other player exactly once. How many games are played in total?
6 · Round-robin & network conn…
2. In a round-robin tournament with 9 players, every player plays every other player exactly once. How many games are played in total?
9 · Round-robin & network conn…
3. In a round-robin tournament with 13 players, every player plays every other player exactly once. How many games are played in total?
13 · Round-robin & network conn…
4. In a round-robin tournament with 30 players, every player plays every other player exactly once. How many games are played in total?
30 · Round-robin & network conn…
5. In a round-robin tournament with 7 players, every player plays every other player exactly once. How many games are played in total?
7 · Round-robin & network conn…
6. In a round-robin tournament with 17 players, every player plays every other player exactly once. How many games are played in total?
17 · Round-robin & network conn…
7. In a round-robin tournament with 11 players, every player plays every other player exactly once. How many games are played in total?
11 · Round-robin & network conn…
8. In a round-robin tournament with 8 players, every player plays every other player exactly once. How many games are played in total?
8 · Round-robin & network conn…
9. In a round-robin tournament with 12 players, every player plays every other player exactly once. How many games are played in total?
12 · Round-robin & network conn…
10. In a round-robin tournament with 10 players, every player plays every other player exactly once. How many games are played in total?
10 · Round-robin & network conn…
11. In a round-robin tournament with 21 players, every player plays every other player exactly once. How many games are played in total?
21 · Round-robin & network conn…
12. In a round-robin tournament with 4 players, every player plays every other player exactly once. How many games are played in total?
4 · Round-robin & network conn…

12 questions · Seed 54 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Round-robin & network connections

Answers and reasoning. Review before teaching.

1. In a round-robin tournament with 6 players, every player plays every other player exactly once. How many games are played in total?
15
Each of the 6 players plays 5 others, and dividing by 2 avoids double-counting: (6 × 5) ÷ 2 = 15 games.
2. In a round-robin tournament with 9 players, every player plays every other player exactly once. How many games are played in total?
36
Each of the 9 players plays 8 others, and dividing by 2 avoids double-counting: (9 × 8) ÷ 2 = 36 games.
3. In a round-robin tournament with 13 players, every player plays every other player exactly once. How many games are played in total?
78
Each of the 13 players plays 12 others, and dividing by 2 avoids double-counting: (13 × 12) ÷ 2 = 78 games.
4. In a round-robin tournament with 30 players, every player plays every other player exactly once. How many games are played in total?
435
Each of the 30 players plays 29 others, and dividing by 2 avoids double-counting: (30 × 29) ÷ 2 = 435 games.
5. In a round-robin tournament with 7 players, every player plays every other player exactly once. How many games are played in total?
21
Each of the 7 players plays 6 others, and dividing by 2 avoids double-counting: (7 × 6) ÷ 2 = 21 games.
6. In a round-robin tournament with 17 players, every player plays every other player exactly once. How many games are played in total?
136
Each of the 17 players plays 16 others, and dividing by 2 avoids double-counting: (17 × 16) ÷ 2 = 136 games.
7. In a round-robin tournament with 11 players, every player plays every other player exactly once. How many games are played in total?
55
Each of the 11 players plays 10 others, and dividing by 2 avoids double-counting: (11 × 10) ÷ 2 = 55 games.
8. In a round-robin tournament with 8 players, every player plays every other player exactly once. How many games are played in total?
28
Each of the 8 players plays 7 others, and dividing by 2 avoids double-counting: (8 × 7) ÷ 2 = 28 games.
9. In a round-robin tournament with 12 players, every player plays every other player exactly once. How many games are played in total?
66
Each of the 12 players plays 11 others, and dividing by 2 avoids double-counting: (12 × 11) ÷ 2 = 66 games.
10. In a round-robin tournament with 10 players, every player plays every other player exactly once. How many games are played in total?
45
Each of the 10 players plays 9 others, and dividing by 2 avoids double-counting: (10 × 9) ÷ 2 = 45 games.
11. In a round-robin tournament with 21 players, every player plays every other player exactly once. How many games are played in total?
210
Each of the 21 players plays 20 others, and dividing by 2 avoids double-counting: (21 × 20) ÷ 2 = 210 games.
12. In a round-robin tournament with 4 players, every player plays every other player exactly once. How many games are played in total?
6
Each of the 4 players plays 3 others, and dividing by 2 avoids double-counting: (4 × 3) ÷ 2 = 6 games.

12 questions · Seed 54 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Round-robin & network connections

Take your time. Show your thinking.

1. In a round-robin tournament with 6 players, every player plays every other player exactly once. How many games are played in total?
6 · Round-robin & network conn…
2. In a round-robin tournament with 9 players, every player plays every other player exactly once. How many games are played in total?
9 · Round-robin & network conn…
3. In a round-robin tournament with 13 players, every player plays every other player exactly once. How many games are played in total?
13 · Round-robin & network conn…
4. In a round-robin tournament with 30 players, every player plays every other player exactly once. How many games are played in total?
30 · Round-robin & network conn…
5. In a round-robin tournament with 7 players, every player plays every other player exactly once. How many games are played in total?
7 · Round-robin & network conn…
6. In a round-robin tournament with 17 players, every player plays every other player exactly once. How many games are played in total?
17 · Round-robin & network conn…
7. In a round-robin tournament with 11 players, every player plays every other player exactly once. How many games are played in total?
11 · Round-robin & network conn…
8. In a round-robin tournament with 8 players, every player plays every other player exactly once. How many games are played in total?
8 · Round-robin & network conn…
9. In a round-robin tournament with 12 players, every player plays every other player exactly once. How many games are played in total?
12 · Round-robin & network conn…
10. In a round-robin tournament with 10 players, every player plays every other player exactly once. How many games are played in total?
10 · Round-robin & network conn…
11. In a round-robin tournament with 21 players, every player plays every other player exactly once. How many games are played in total?
21 · Round-robin & network conn…
12. In a round-robin tournament with 4 players, every player plays every other player exactly once. How many games are played in total?
4 · Round-robin & network conn…

12 questions · Seed 54 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Round-robin & network connections

Answers and reasoning. Review before teaching.

1. In a round-robin tournament with 6 players, every player plays every other player exactly once. How many games are played in total?
15
Each of the 6 players plays 5 others, and dividing by 2 avoids double-counting: (6 × 5) ÷ 2 = 15 games.
2. In a round-robin tournament with 9 players, every player plays every other player exactly once. How many games are played in total?
36
Each of the 9 players plays 8 others, and dividing by 2 avoids double-counting: (9 × 8) ÷ 2 = 36 games.
3. In a round-robin tournament with 13 players, every player plays every other player exactly once. How many games are played in total?
78
Each of the 13 players plays 12 others, and dividing by 2 avoids double-counting: (13 × 12) ÷ 2 = 78 games.
4. In a round-robin tournament with 30 players, every player plays every other player exactly once. How many games are played in total?
435
Each of the 30 players plays 29 others, and dividing by 2 avoids double-counting: (30 × 29) ÷ 2 = 435 games.
5. In a round-robin tournament with 7 players, every player plays every other player exactly once. How many games are played in total?
21
Each of the 7 players plays 6 others, and dividing by 2 avoids double-counting: (7 × 6) ÷ 2 = 21 games.
6. In a round-robin tournament with 17 players, every player plays every other player exactly once. How many games are played in total?
136
Each of the 17 players plays 16 others, and dividing by 2 avoids double-counting: (17 × 16) ÷ 2 = 136 games.
7. In a round-robin tournament with 11 players, every player plays every other player exactly once. How many games are played in total?
55
Each of the 11 players plays 10 others, and dividing by 2 avoids double-counting: (11 × 10) ÷ 2 = 55 games.
8. In a round-robin tournament with 8 players, every player plays every other player exactly once. How many games are played in total?
28
Each of the 8 players plays 7 others, and dividing by 2 avoids double-counting: (8 × 7) ÷ 2 = 28 games.
9. In a round-robin tournament with 12 players, every player plays every other player exactly once. How many games are played in total?
66
Each of the 12 players plays 11 others, and dividing by 2 avoids double-counting: (12 × 11) ÷ 2 = 66 games.
10. In a round-robin tournament with 10 players, every player plays every other player exactly once. How many games are played in total?
45
Each of the 10 players plays 9 others, and dividing by 2 avoids double-counting: (10 × 9) ÷ 2 = 45 games.
11. In a round-robin tournament with 21 players, every player plays every other player exactly once. How many games are played in total?
210
Each of the 21 players plays 20 others, and dividing by 2 avoids double-counting: (21 × 20) ÷ 2 = 210 games.
12. In a round-robin tournament with 4 players, every player plays every other player exactly once. How many games are played in total?
6
Each of the 4 players plays 3 others, and dividing by 2 avoids double-counting: (4 × 3) ÷ 2 = 6 games.

12 questions · Seed 54 · Age guidance, not curriculum certification