The Clockmaker's Birthday Cake

'The Clockmaker's Birthday Cake' printed from https://nrich.maths.org/

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The Clockmaker's Birthday Cake

The clockmaker's wife was a mathematician. On his birthday she invited five other couples to tea. She made a birthday cake decorated to look like a clock face with numbers made from pink icing.

She cut up the cake into twelve slices with a number on each slice:

cake cut into 12 slices with each slice having a number between 1 and 12 on it

The slices that she gave each couple added to the same number. What was the number?

The clockmaker had the slice with $12$ on it because it was his birthday. One guest wanted $7$ because it was her lucky number. All the slices that went to men added to a number equal to those that went to the women.

How could this be arranged?

Why do this problem?

This problem practises addition, subtraction, multiplication and division in an interesting and thought-provoking way.

Key questions

What do all the numbers on the cake add to?

How many couples are there?

How can you use this total to work out the sum of the numbers on each couple's slices?

Possible extension

Learners who found the problem easy might like to try this one .

Possible support

A good place to start might be to suggest pupils work out (with a calculator if necessary) the sum of all the numbers on the cake.