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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:

cake cut into 12 slices with each slice having a number between 1 and 12 on it

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?