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 Mikey from the Archbishop
of York Junior School who sent in the following solution based on
We started off by thinking of 6 different objects and how many
different ways there are of arranging them.
This gives 6 $\times$5 $\times$4
$\times$3 $\times$2 $\times$1 =
720 ways of arranging 6 different coloured balls.
But 3 of our balls are red - they can be arranged in 3
$\times$2 $\times$1 = 6 different ways that
all look the same. (ABC, ACB, BAC, BCA, CBA, CAB)
Similarly there are 2 identical blue balls that can be arranged
in 2 $\times$1 = 2 different ways that look the same.
So although we have 720 different ways of arranging the balls
only so many of them will look different in this question.
There are 720 / (6 $\times$2) different looking ways
of arranging the balls in this question, giving 60 different
At first we thought there was only one way for the reds to all
lose and that is for them to be in the middle of each side. But
then we realised that the corner 3 balls could be arranged
differently with the yellow ball in each of the 3 corners.
Hence there are 3 different ways to lose out of 60, or more
simply 1 expected loss in every 20, ie 5% loss, 95% win.
The online scenario tester supports the 0.95, 95% chance of