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?