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'Sociable Cards' printed from http://nrich.maths.org/
Take a pack of cards and remove the Jacks, Queens and Kings.
Shuffle the remaining cards, and then lay the whole pack face up on
the table in a snake, like this one:
Place four different coloured counters on the first four cards in
the snake. Then move each counter foward the number shown on its
card (Aces count as $1$). Keep moving each counter until it can't
go any further without going off the end.
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Did your counters all finish on different cards?
Repeat the experiment a few times.
How often did all the counters finish on different cards?
How often did they all finish on the same card?
Can you explain your results?
Find a way to arrange the cards so that all four counters finish on
Can you do the same with five counters?
This problem is based on a card
trick called Kruskal's Count; you can read more about the original
this article by Steve Humble.