**4th puzzle by Dr Harry Wiggins**

It is Nxolo's birthday. She has one big cake and wants to divide it into the many pieces. She knows the number of people at her birthday party is either 20 or 18. What is the **least number of pieces**, she has to divide her cake so that in either case, she will be able to give everybody the same amount of cake? And how can she achieve this? (Hint: Fractions!)

CommentsLet the minimum number of pieces be x. We know that x/20 is an integer, and so is x/18. This means that 18 and 20 are factors of x. LCM(18, 20) = 180, so therefore the minimum number of pieces needed is 180.

She can achieve this by cutting 180 equally sized pieces using a protractor or something

Sachin Reddy Northwood School

(Hint: All the pieces does not have to be the same size. )

When there are 18 people, she just needs to give each person a big slice and a small slice and then everyone has 1/18 of the cake

When there are 20 people, she gives the first 18 people a big slice each, and then the remaining 2 people each 9 small slice. This way, everyone has 1/20 of the cake