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 21 players, every player plays every other player exactly once. How many games are played in total?
21 · Round-robin & network conn…
2. 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…
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 26 players, every player plays every other player exactly once. How many games are played in total?
26 · Round-robin & network conn…
5. 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…
6. 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…
7. 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…
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 27 players, every player plays every other player exactly once. How many games are played in total?
27 · Round-robin & network conn…
10. 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…
11. In a round-robin tournament with 24 players, every player plays every other player exactly once. How many games are played in total?
24 · Round-robin & network conn…
12. 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…

12 questions · Seed 45 · 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 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.
2. 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.
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 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.
5. 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.
6. 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.
7. 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.
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 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.
10. 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.
11. In a round-robin tournament with 24 players, every player plays every other player exactly once. How many games are played in total?
276
Each of the 24 players plays 23 others, and dividing by 2 avoids double-counting: (24 × 23) ÷ 2 = 276 games.
12. 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.

12 questions · Seed 45 · 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 21 players, every player plays every other player exactly once. How many games are played in total?
21 · Round-robin & network conn…
2. 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…
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 26 players, every player plays every other player exactly once. How many games are played in total?
26 · Round-robin & network conn…
5. 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…
6. 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…
7. 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…
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 27 players, every player plays every other player exactly once. How many games are played in total?
27 · Round-robin & network conn…
10. 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…
11. In a round-robin tournament with 24 players, every player plays every other player exactly once. How many games are played in total?
24 · Round-robin & network conn…
12. 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…

12 questions · Seed 45 · 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 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.
2. 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.
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 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.
5. 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.
6. 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.
7. 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.
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 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.
10. 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.
11. In a round-robin tournament with 24 players, every player plays every other player exactly once. How many games are played in total?
276
Each of the 24 players plays 23 others, and dividing by 2 avoids double-counting: (24 × 23) ÷ 2 = 276 games.
12. 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.

12 questions · Seed 45 · Age guidance, not curriculum certification