A monk starts his journey from the base of the mountain early morning at 7 am and reaches the monastery at the top of the mountain at 7 pm. He followed the hilly route at a completely variable speed. He sometimes sat down to take rest too. He was fast at times and slow at other times. After giving the necessary message to the head monk, next day, fully rested, he started at 8 am to climb down. Once again, he walked at varying speed including taking rest at times. Since it was downhill though, he reached by 6pm. Can you prove that there was at least one clock time where on either day at the same clock time, he was at the same spot? [note that you do not need to find out when and where – that is indeterminate – just that there had to be a time when on either day at that time he was at the same spot]