27 Mar '07 15:192 edits

Take a pack of 52 cards with 3 jokers, so there are 55 cards. Put them in piles with any number of cards in each pile. Take 1 card from each pile and make a new one. Keep repeating this - what do you end up with? Can you show that this always happens from any initial configuration (describing an algorithm that could be implemented on a computer is sufficient)?

To illustrate what is happening - say you start with 4 piles, a pile of 44, one with only 1 card in and the other two piles both with 5 cards:

44, 5, 5, 1 ---> 43, 4, 4, 0, 4 = 43, 4, 4, 4 ---> 42, 3, 3, 3, 4 ---> 41, 2, 2, 2, 3, 5 etc.

I orginally heard this one on the BBC Radio 4 program Puzzle Panel.

To illustrate what is happening - say you start with 4 piles, a pile of 44, one with only 1 card in and the other two piles both with 5 cards:

44, 5, 5, 1 ---> 43, 4, 4, 0, 4 = 43, 4, 4, 4 ---> 42, 3, 3, 3, 4 ---> 41, 2, 2, 2, 3, 5 etc.

I orginally heard this one on the BBC Radio 4 program Puzzle Panel.