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

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:

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?