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The Lady or the Lions

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?

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Master Minding

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

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Flippin' Discs

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Two's Company

Age 11 to 14 Challenge Level:

A container holds $4$ yellow marbles, $2$ blue marbles and $1$ red marble.
The marbles are identical in all ways except colour.
Shake the container, and look at how the marbles settle.

You win if two blue marbles touch.

Did you win?
Complete several shakes and look at your results.

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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.

Can you explain how to work out the theoretical probability of winning?

You may find these sheets useful if you want to work on paper or submit a solution.