The Christmas cookie dice game
Author: Christian Schröder
Project: SE 1
Problem
Three of Santa’s elves ask him for some of his famous delicious Christmas
cookies. They crave them so much that even just thinking of them makes
their mouth water. Santa agrees, but only under the rules of a dice game.
The game starts with six empty plates, numbered one through six. The elves
take turns rolling a fair dice. The rolled number, say a five, corresponds to
a plate, here the fifth plate. In the beginning, this plate is empty. Santa
places a cookie on it. Then the next elf rolls the die. Should the plate that
corresponds to the rolled number contain a cookie, the elf may have it. But
if that plate is empty, Santa will put a cookie there. Either way, now it’s the
next elf’s turn. The game continues as described as long as there is at least
one empty plate. The game ends when a new cookie fills the last empty plate.
In this case the previous rolling elf may eat all six cookies and the elves may
go back to work.
On average, how many cookies will be eaten in total during this game?
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Possible Answers:
1. 6
2. 6.3
3. 12
4. 27.2
5. 31.4
6. 42
7. 44.6
8. 47
9. 83.2
10. infinitely many
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