This problem solving activity has an algebra focus.
Six business people meet for lunch and shake hands with each other.
How many handshakes are there?
The maths that is involved in this problem depends on the approach that is used to solve it. If the students look for patterns starting with the simpler cases (2 people etc) the problem involves triangular numbers.
Six business people meet for lunch and shake hands with each other. How many handshakes are there?
How many handshakes are there at the meeting if people come in pairs and shake hands with everyone except their own partners.
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.
6 people = 12 handshakes (15 – 3 = 12, subtract 3 for the shakes that are between partners).
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/shaking-hands at 8:56pm on the 26th February 2024