ReasoningAges 13-15

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 13-15

Round-robin & network connections

Take your time. Show your thinking.

1. 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…
2. In a round-robin tournament with 27 players, every player plays every other player exactly once. How many games are played in total?
27 · Round-robin & network conn…
3. In a round-robin tournament with 19 players, every player plays every other player exactly once. How many games are played in total?
19 · 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 10 players, every player plays every other player exactly once. How many games are played in total?
10 · Round-robin & network conn…
6. 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…
7. 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…
8. 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…
9. 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…
10. 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…
11. 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…
12. 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…

12 questions · Seed 53 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Round-robin & network connections

Answers and reasoning. Review before teaching.

1. 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.
2. In a round-robin tournament with 27 players, every player plays every other player exactly once. How many games are played in total?
351
Each of the 27 players plays 26 others, and dividing by 2 avoids double-counting: (27 × 26) ÷ 2 = 351 games.
3. In a round-robin tournament with 19 players, every player plays every other player exactly once. How many games are played in total?
171
Each of the 19 players plays 18 others, and dividing by 2 avoids double-counting: (19 × 18) ÷ 2 = 171 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 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Round-robin & network connections

Take your time. Show your thinking.

1. 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…
2. In a round-robin tournament with 27 players, every player plays every other player exactly once. How many games are played in total?
27 · Round-robin & network conn…
3. In a round-robin tournament with 19 players, every player plays every other player exactly once. How many games are played in total?
19 · 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 10 players, every player plays every other player exactly once. How many games are played in total?
10 · Round-robin & network conn…
6. 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…
7. 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…
8. 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…
9. 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…
10. 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…
11. 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…
12. 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…

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Round-robin & network connections

Answers and reasoning. Review before teaching.

1. 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.
2. In a round-robin tournament with 27 players, every player plays every other player exactly once. How many games are played in total?
351
Each of the 27 players plays 26 others, and dividing by 2 avoids double-counting: (27 × 26) ÷ 2 = 351 games.
3. In a round-robin tournament with 19 players, every player plays every other player exactly once. How many games are played in total?
171
Each of the 19 players plays 18 others, and dividing by 2 avoids double-counting: (19 × 18) ÷ 2 = 171 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 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification