Question

If six (6) people greet each other at a meeting by shaking hands with one another, how many handshakes will take place?

UNDERSTANDING THE PROBLEM:



DEVISE A PLAN:



CARRY OUT THE PLAN:



REVISE THE SOLUTION:

Answer 1

15

Explanation:

If two people shake hands there is one handshake.

If three people shake hands there are 3 handshakes.

If four people shake hands there are 3 more handshakes so 3 + 3 = 6 in total.

If five people shake hands there are another 4 handshakes so 6 + 4 = 10.

For 6 people there are another 5 handshakes so 10 + 5 = 15.

A second pattern that may be described is that each person has to shake hands with all the others. If there are 6 people each person has 5 handshakes to make. But each time a handshake occurs there are 2 people involved. This means that you only need ½ (6 x 5 ) = 15.