Rabbit’s Card Puzzle
31/08/2010 13 Comments
Two people sit down at a table, each with a shuffled pack of standard playing cards in front of them.
They each turn over the top card and place it face up on the table. If they have the same card they shout “SNAP!”
For this to occur both number and suit must match. Four of Spades does NOT match with Four of Hearts.
The chances of this happening on the first go is 1 in 52.
Now more people want to join this fantastic game. Each time a new player joins they bring their own pack of shuffled cards.
i.e. When there are 4 players, 4 cards are turned over. If there is a pair anywhere among the 4 cards they all shout “SNAP!”
As the size of the group increases, the chances of shouting “SNAP!” increases.
At some point the group becomes so large that it is more likely than not that “SNAP!” will be shouted when they each turn their first card over.
What is the smallest number of players required to make it more likely than not that “SNAP!” will be shouted when they each turn their first card over?
I will donate £10 to the chosen charity of the person with the first correct answer.
They need a rough reason though. You can’t just guess 1,2,3,4 etc. until you get the right number.
Please put your answer in the comments on this post, not on Twitter.