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?