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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?

What Does Random Look Like?

Stage: 3 Challenge Level: Challenge Level:1

On a strip like the one below, ask a friend to make up a sequence of twenty Hs and Ts that could represent a sequence of heads and tails generated by a fair coin, and ask them to write "made up" lightly in pencil on the back of the strip.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Then ask your friend to flip a fair coin twenty times and record the results on a second strip, and this time ask them to write "real" lightly in pencil on the back.
Take the two strips and try to work out which was real and which was made up - you could create similar strips and challenge your friend in the same way.
Here is an animation which generates twenty random coin flips. Hover over the bars on the bar chart to see how the runs have been counted.
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Use the animation to generate several sequences of twenty coin flips, and try to get a feel for the features you would expect a random sequence to have.

How would you analyse whether a sequence came from a real coin?
Send us your ideas and justify the method you use to decide.

Are you now better at spotting fakes? Ask your friend to create two more strips and see if you can find the truly random one.