Handshakes & Matches

Handshakes and round-robin matches count pairs. Among n people, the number of pairs is n(n − 1) ÷ 2.

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1. Q1Medium

   4 friends each shake hands once with every other. How many handshakes?

   1. A16
   2. B12
   3. C6
   4. D10
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   Answer: C. 6

   💡 Each pair meets once: 4 × 3 ÷ 2 = 6.

2. Q2Medium

   14 friends each shake hands once with every other. How many handshakes?

   1. A19
   2. B196
   3. C91
   4. D73
   Show answer

   Answer: C. 91

   💡 Each pair meets once: 14 × 13 ÷ 2 = 91.

3. Q3Medium

   14 teams each play every other team once. How many matches?

   1. A182
   2. B91
   3. C81
   4. D73
   Show answer

   Answer: B. 91

   💡 Each pair meets once: 14 × 13 ÷ 2 = 91.

4. Q4Medium

   15 friends each shake hands once with every other. How many handshakes?

   1. A95
   2. B101
   3. C210
   4. D105
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   Answer: D. 105

   💡 Each pair meets once: 15 × 14 ÷ 2 = 105.

5. Q5Hard

   At a party, everyone shook hands once with everyone else: 78 handshakes in all. How many people?

   1. A12
   2. B10
   3. C13
   4. D9
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   Answer: C. 13

   💡 n × (n − 1) ÷ 2 = 78 gives n = 13.

6. Q6Hard

   At a party, everyone shook hands once with everyone else: 66 handshakes in all. How many people?

   1. A11
   2. B15
   3. C14
   4. D12
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   Answer: D. 12

   💡 n × (n − 1) ÷ 2 = 66 gives n = 12.

7. Q7Hard

   In a league of 4 teams, each team plays every other team twice. How many matches?

   1. A16
   2. B15
   3. C12
   4. D21
   Show answer

   Answer: C. 12

   💡 4 × 3 ÷ 2 = 6 pairs, each playing twice: 12 matches.

8. Q8Hard

   In a league of 5 teams, each team plays every other team twice. How many matches?

   1. A18
   2. B17
   3. C20
   4. D10
   Show answer

   Answer: C. 20

   💡 5 × 4 ÷ 2 = 10 pairs, each playing twice: 20 matches.