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 29 players, every player plays every other player exactly once. How many games are played in total?
29 · Round-robin & network conn…
2. 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…
3. 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…
4. In a round-robin tournament with 22 players, every player plays every other player exactly once. How many games are played in total?
22 · Round-robin & network conn…
5. 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…
6. In a round-robin tournament with 16 players, every player plays every other player exactly once. How many games are played in total?
16 · Round-robin & network conn…
7. In a round-robin tournament with 18 players, every player plays every other player exactly once. How many games are played in total?
18 · Round-robin & network conn…
8. 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…
9. In a round-robin tournament with 26 players, every player plays every other player exactly once. How many games are played in total?
26 · Round-robin & network conn…
10. 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…
11. In a round-robin tournament with 23 players, every player plays every other player exactly once. How many games are played in total?
23 · Round-robin & network conn…
12. 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…

12 questions · Seed 61 · 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 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.
2. 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.
3. 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.
4. In a round-robin tournament with 22 players, every player plays every other player exactly once. How many games are played in total?
231
Each of the 22 players plays 21 others, and dividing by 2 avoids double-counting: (22 × 21) ÷ 2 = 231 games.
5. 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.
6. In a round-robin tournament with 16 players, every player plays every other player exactly once. How many games are played in total?
120
Each of the 16 players plays 15 others, and dividing by 2 avoids double-counting: (16 × 15) ÷ 2 = 120 games.
7. In a round-robin tournament with 18 players, every player plays every other player exactly once. How many games are played in total?
153
Each of the 18 players plays 17 others, and dividing by 2 avoids double-counting: (18 × 17) ÷ 2 = 153 games.
8. 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.
9. In a round-robin tournament with 26 players, every player plays every other player exactly once. How many games are played in total?
325
Each of the 26 players plays 25 others, and dividing by 2 avoids double-counting: (26 × 25) ÷ 2 = 325 games.
10. 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.
11. In a round-robin tournament with 23 players, every player plays every other player exactly once. How many games are played in total?
253
Each of the 23 players plays 22 others, and dividing by 2 avoids double-counting: (23 × 22) ÷ 2 = 253 games.
12. 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.

12 questions · Seed 61 · 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 29 players, every player plays every other player exactly once. How many games are played in total?
29 · Round-robin & network conn…
2. 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…
3. 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…
4. In a round-robin tournament with 22 players, every player plays every other player exactly once. How many games are played in total?
22 · Round-robin & network conn…
5. 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…
6. In a round-robin tournament with 16 players, every player plays every other player exactly once. How many games are played in total?
16 · Round-robin & network conn…
7. In a round-robin tournament with 18 players, every player plays every other player exactly once. How many games are played in total?
18 · Round-robin & network conn…
8. 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…
9. In a round-robin tournament with 26 players, every player plays every other player exactly once. How many games are played in total?
26 · Round-robin & network conn…
10. 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…
11. In a round-robin tournament with 23 players, every player plays every other player exactly once. How many games are played in total?
23 · Round-robin & network conn…
12. 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…

12 questions · Seed 61 · 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 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.
2. 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.
3. 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.
4. In a round-robin tournament with 22 players, every player plays every other player exactly once. How many games are played in total?
231
Each of the 22 players plays 21 others, and dividing by 2 avoids double-counting: (22 × 21) ÷ 2 = 231 games.
5. 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.
6. In a round-robin tournament with 16 players, every player plays every other player exactly once. How many games are played in total?
120
Each of the 16 players plays 15 others, and dividing by 2 avoids double-counting: (16 × 15) ÷ 2 = 120 games.
7. In a round-robin tournament with 18 players, every player plays every other player exactly once. How many games are played in total?
153
Each of the 18 players plays 17 others, and dividing by 2 avoids double-counting: (18 × 17) ÷ 2 = 153 games.
8. 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.
9. In a round-robin tournament with 26 players, every player plays every other player exactly once. How many games are played in total?
325
Each of the 26 players plays 25 others, and dividing by 2 avoids double-counting: (26 × 25) ÷ 2 = 325 games.
10. 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.
11. In a round-robin tournament with 23 players, every player plays every other player exactly once. How many games are played in total?
253
Each of the 23 players plays 22 others, and dividing by 2 avoids double-counting: (23 × 22) ÷ 2 = 253 games.
12. 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.

12 questions · Seed 61 · Age guidance, not curriculum certification