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 7 players, every player plays every other player exactly once. How many games are played in total?
7 · 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 17 players, every player plays every other player exactly once. How many games are played in total?
17 · Round-robin & network conn…
4. 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…
5. In a round-robin tournament with 5 players, every player plays every other player exactly once. How many games are played in total?
5 · Round-robin & network conn…
6. In a round-robin tournament with 20 players, every player plays every other player exactly once. How many games are played in total?
20 · Round-robin & network conn…
7. In a round-robin tournament with 25 players, every player plays every other player exactly once. How many games are played in total?
25 · Round-robin & network conn…
8. 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…
9. In a round-robin tournament with 15 players, every player plays every other player exactly once. How many games are played in total?
15 · Round-robin & network conn…
10. In a round-robin tournament with 29 players, every player plays every other player exactly once. How many games are played in total?
29 · Round-robin & network conn…
11. 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…
12. In a round-robin tournament with 14 players, every player plays every other player exactly once. How many games are played in total?
14 · Round-robin & network conn…

12 questions · Seed 104733 · 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 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.
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 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.
4. 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.
5. In a round-robin tournament with 5 players, every player plays every other player exactly once. How many games are played in total?
10
Each of the 5 players plays 4 others, and dividing by 2 avoids double-counting: (5 × 4) ÷ 2 = 10 games.
6. In a round-robin tournament with 20 players, every player plays every other player exactly once. How many games are played in total?
190
Each of the 20 players plays 19 others, and dividing by 2 avoids double-counting: (20 × 19) ÷ 2 = 190 games.
7. In a round-robin tournament with 25 players, every player plays every other player exactly once. How many games are played in total?
300
Each of the 25 players plays 24 others, and dividing by 2 avoids double-counting: (25 × 24) ÷ 2 = 300 games.
8. 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.
9. In a round-robin tournament with 15 players, every player plays every other player exactly once. How many games are played in total?
105
Each of the 15 players plays 14 others, and dividing by 2 avoids double-counting: (15 × 14) ÷ 2 = 105 games.
10. In a round-robin tournament with 29 players, every player plays every other player exactly once. How many games are played in total?
406
Each of the 29 players plays 28 others, and dividing by 2 avoids double-counting: (29 × 28) ÷ 2 = 406 games.
11. 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.
12. In a round-robin tournament with 14 players, every player plays every other player exactly once. How many games are played in total?
91
Each of the 14 players plays 13 others, and dividing by 2 avoids double-counting: (14 × 13) ÷ 2 = 91 games.

12 questions · Seed 104733 · 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 7 players, every player plays every other player exactly once. How many games are played in total?
7 · 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 17 players, every player plays every other player exactly once. How many games are played in total?
17 · Round-robin & network conn…
4. 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…
5. In a round-robin tournament with 5 players, every player plays every other player exactly once. How many games are played in total?
5 · Round-robin & network conn…
6. In a round-robin tournament with 20 players, every player plays every other player exactly once. How many games are played in total?
20 · Round-robin & network conn…
7. In a round-robin tournament with 25 players, every player plays every other player exactly once. How many games are played in total?
25 · Round-robin & network conn…
8. 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…
9. In a round-robin tournament with 15 players, every player plays every other player exactly once. How many games are played in total?
15 · Round-robin & network conn…
10. In a round-robin tournament with 29 players, every player plays every other player exactly once. How many games are played in total?
29 · Round-robin & network conn…
11. 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…
12. In a round-robin tournament with 14 players, every player plays every other player exactly once. How many games are played in total?
14 · Round-robin & network conn…

12 questions · Seed 104733 · 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 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.
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 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.
4. 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.
5. In a round-robin tournament with 5 players, every player plays every other player exactly once. How many games are played in total?
10
Each of the 5 players plays 4 others, and dividing by 2 avoids double-counting: (5 × 4) ÷ 2 = 10 games.
6. In a round-robin tournament with 20 players, every player plays every other player exactly once. How many games are played in total?
190
Each of the 20 players plays 19 others, and dividing by 2 avoids double-counting: (20 × 19) ÷ 2 = 190 games.
7. In a round-robin tournament with 25 players, every player plays every other player exactly once. How many games are played in total?
300
Each of the 25 players plays 24 others, and dividing by 2 avoids double-counting: (25 × 24) ÷ 2 = 300 games.
8. 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.
9. In a round-robin tournament with 15 players, every player plays every other player exactly once. How many games are played in total?
105
Each of the 15 players plays 14 others, and dividing by 2 avoids double-counting: (15 × 14) ÷ 2 = 105 games.
10. In a round-robin tournament with 29 players, every player plays every other player exactly once. How many games are played in total?
406
Each of the 29 players plays 28 others, and dividing by 2 avoids double-counting: (29 × 28) ÷ 2 = 406 games.
11. 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.
12. In a round-robin tournament with 14 players, every player plays every other player exactly once. How many games are played in total?
91
Each of the 14 players plays 13 others, and dividing by 2 avoids double-counting: (14 × 13) ÷ 2 = 91 games.

12 questions · Seed 104733 · Age guidance, not curriculum certification