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Snail Trails

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in a straight line. Move only vertically (up/down) or horizontally (across), never diagonally. You can cross over the other player's trails. You can trace over the top of the other player's trails. You can cross over a single trail of your own, but can never cross a pair of your trails (side-by-side) or trace over your own trail. To win, you must roll the exact number needed to finish in the target square. You can never pass through the target square. The game ends when a player ends his/her trail in the target square, OR when a player cannot move without breaking any of the rules.

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Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Sociable Cards

Stage: 3 Challenge Level: Challenge Level:1

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:
 
snake of cards
 
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?
 
Challenge
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; you can read more about the original trick in this article by Steve Humble.