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The Clockmaker's Birthday Cake

Stage: 2 Challenge Level: Challenge Level:1

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