This is not the hardest puzzle ever set, but that does not stop it from offering some enjoyable insight onto our assumptions about the way the world works.
A buddhist monk sets off to reach the top of a mountain, walking up a single winding path, slowing, stopping and starting at will, before spending the night at the summit. He sets off back down the mountain at exactly the same time as he set off the day before. Can you show that at some instant during his descent he is at the same place at the same time as he was the day before?
Reveal solution
The solution offered by puzzle’s original setter, the legend of brain tease Martin Gardiner, is that we should imagine there are two monks setting off from the top and bottom of the mountain at the same time on the same day. Their journies must inevitably cross at some point and this would, naturally, have to be at the same place and at the same time. This is an extremely concise and elegant solution, but it is also hard for me to picture and why should we have to shift timeframe and imagine two monks?
It was easier for me to draw a graph of distance up the path and time, zeroed at the time the monk sets off each day (see right). If you try drawing wiggly lines between the top of the mountain and the bottom and bottom to top, you will find they have to cross. This crossing point means the monk is at the same place at the same time of day on both days.
We might also notice, using this method, that the paths can be made not to cross if we had a rogue monk who retreated below the starting point on day one until after the time he returns on day two (see left). Or he might do something similar by setting off then simply levitating above the summit on day two until after his arrival time on day one.
Allowing monks to participate who had the ability to disappear and reappear again would also mess up the argument (see right). It is not the hardest puzzle ever, but this does not stop it from asking us to question our assumptions. ■
