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 marble falls into the centre, the other blue marble can fall into any of the 6 positions on the outside ring.
If there is no blue marble in the centre, the two blue marbles can fall into the following 15 positions:
AB, AC, AD, AE, AF
BC, BD, BE, BF
CD, CE, CF
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 marble falls into the centre) and AB, AF, BC, CD, DE and EF.
Congratulations also to Nick from Kegs who had a different approach.