Card game
Author: Onno Boxma (TU Eindhoven)
Exercise
The Grinch has a set of cards containing 16 cards which are numbered from
1 to 16. The cards are shuffled properly by Santa Claus and then split into
two stacks of 8 cards each. Since Santa shuffled the cards fair and square,
every possible distribution of the cards in each pile is equally possible. The
Grinch then gets the first stack and Santa Claus gets the second stack. Both
pick up their cards and look at their hands.
Both players are asked to put one card at a time face up on the table. Santa
Claus lays down the first card. The game ends when the sum of all numbers
on the cards on the table is divisible by 17. The winner is the player who
put the last card on the table. Santa Claus and the Grinch play flawlessly,
so they always perform the best move maximizing their winning chances.
How big is the probability that Santa Claus wins the game?
1
Possible Answers:
1. 0
2. 8! · 8!/16!
3. 1/16!
4. 23/16!
5. 1/17
6. 1/16
7. 1/2
8. 3/4
9. 15/16
10. 1
2