Finding a Hidden Coin

The St. Basil Cake

In the Greek Orthodox tradition, New Year's Day is also the Feast Day of St. Basil (329-379), who was known for his generosity and support of philanthropic projects (Saint Basil Academy [2005]; see Trinity Communications [2006] for a recipe). There are two stories that associate St. Basil with coins in cakes:

• He had cakes baked for the poor and included coins in the cake as a way of helping out those in need.

• When Emperor Valens demanded taxes from his region, Basil gathered jewelry and coins from those who could afford it. But Basil's piety so impressed the emperor's emissary that the items were returned. No record was kept of what belonged to whom, so Basilmade a cake with the materials baked into it. By a miracle, each recipient got the slice with his own items in it. Well, the probability of that is so small that it would indeed be a miracle!

We discuss amathematical problem arising from themodern St. Basil tradition, which calls for the inclusion of a coin in the batter of the St. Basil's Cake, which is also called Vasilopita (also spelled Vasilopitta); the person who gets the coin in his or her slice will have good luck in the coming year. There are apparently two traditions:

• the classic one is to include a coin in the batter, but

• another is to slide the coin under the cake as it is placed on a serving platter.

These versions leads to two distinct mathematical problems, in the style of the Buffon needle problem. Indeed, there is even a third tradition calling for additional trinkets to be baked in the cake, but we will content ourselves with a single coin.