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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

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In how many different positions can the two blue marbles settle?
How many of these positions contain the two marbles touching?

Printing these sheets may be useful if you would like to work on paper and have a go at identifying all the possible positions.