#### You may also like ### Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric. ### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore. ### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

# The Clockmaker's Birthday Cake

##### Age 7 to 11 Challenge Level:

Charles sent in his solution:

All the numbers together add up to $1+2+3+...+12=78$. There are six couples, each with the same total amount, so this must be $78/6=13$. So each couple's numbers add up to $13$.

I'm going to write the pairs in brackets, like this ( , ). The first number is the one for the man, and the second for the woman. So we know we have $(12, 1)$ and $(6, 7)$. We want the ladies' numbers and the men's numbers each to add up to $78/2=39$. Here's a way we could do it:

$(12, 1) (6, 7) (2, 11) (10, 3) (5, 8) (4, 9)$

And $12+6+2+10+5+4=39=1+7+11+3+8+9$.