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Stop or Dare

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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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Odds and Evens

Are these games fair? How can you tell?

Flippin' Discs

Age 11 to 14 Challenge Level:

Imagine you have two discs. Each disc is red on one side and green on the other.

You flip the discs, and when they land, you win if both discs show the same colour.



Click "Run Once" to complete a throw. Did you win?
Click a few more times and look at your results after several throws.

Approximately how often do you think you would win if you completed $100$ throws?
Make a prediction and then check it by doing the experiment.

Now click on the purple cog in the top right corner and change the number of discs to $3$. You win if all the discs show the same colour.

Can you predict what the probability of winning will be this time?
Check that your prediction matches the results from the interactivity.

Do the same with $4$ and $5$ discs.

Do you notice a pattern in your results? Can you explain it?

Can you explain how to find the probability of winning for $n$ discs?