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?
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?
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?
Congratulations to Tom from Colyton Grammar who sent in the correct solution of 4/7:
This is how you can arrive at the 21 combinations:
Let's label the 6 positions on the outside ring A, B, C, D, E and F.
If 1 blue ball falls into the centre, the other blue ball can fall into any of the 6 positions on the outside ring.
If there is no blue ball in the centre, the two blue balls can fall into the following 15 positions: AB, AC, AD, AE, AF BC, BD, BE, BF CD, CE, CF DE, DF EF
This gives a total of 6+5+4+3+2+1 = 21 combinations 12 of these are winning combinations: the first six (when one blue ball falls into the centre) and AB, AF, BC, CD, DE and EF. Congratulations also to Nick from Kegs who had a different approach.