### 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?

There are six different possible ways of choosing two of the loose ends. Only four of these possibilities lead to the ropes being tied together, therefore the probability that Sam holds one piece of rope is $\frac{4}{6}=\frac{2}{3}$.