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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 different cards.
Can you do the same with five counters?
This problem is based on a card trick called Kruskal's Count;