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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Round-robin & network connections

Take your time. Show your thinking.

1. 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…
2. 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…
3. 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…
4. 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…
5. 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…
6. 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…
7. 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…
8. 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…
9. 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…
10. 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…
11. 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…
12. 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…

12 questions · Seed 46 · 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 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 46 · 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 11 players, every player plays every other player exactly once. How many games are played in total?
11 · Round-robin & network conn…
2. 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…
3. 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…
4. 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…
5. 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…
6. 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…
7. 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…
8. 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…
9. 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…
10. 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…
11. 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…
12. 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…

12 questions · Seed 46 · 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 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 46 · Age guidance, not curriculum certification