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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?

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?

Flippin' Discs

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

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.
Run the interactivity below to simulate shaking the container.

You win if two blue marbles touch.

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

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 find a way of working out the theoretical probability of winning?

You may find this Recording Sheet useful.