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Handshakes – practice for Years 5–9

Sample questions on Handshakes with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Logic
Year
Years 5–9
Curriculum area
Counting

Question types: Everyone with everyone

Rule: Handshakes

When n people all shake hands, there are n × (n − 1) ÷ 2 handshakes: each meets n − 1 others, and each is counted twice.

A tournament where everyone plays everyone: the same. Home and away: n × (n − 1). An n-sided shape has n × (n − 3) ÷ 2 diagonals.

Example: 5 friends: 5 × 4 ÷ 2 = 10 handshakes.

Watch out: Don’t forget to halve: Ann shaking hands with Bea is the same as Bea shaking hands with Ann.

Sample questions

  1. Question 1 Easy

    7 friends met at a party. Everyone shook hands with everyone else exactly once. How many handshakes were there?

    Show the solution
    Answer: 21

    How it works: 7 · 6 : 2 = 21

  2. Question 2 Normal

    16 teams play in a tournament; every team plays every other team once. How many matches are played?

    Show the solution
    Answer: 120

    How it works: 16 · 15 : 2 = 120

  3. Question 3 Hard

    At a meeting everyone shook hands with everyone else exactly once. There were 190 handshakes in all. How many people were at the meeting?

    Show the solution
    Answer: 20

    How it works: 20 · 19 : 2 = 190

Related topics

All Logic topics

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