Another unforgettable problem is the following problem from the Canadian Mathematical Olympiad in 1989. Although I did not participate in that year's competition, I came across it as I was preparing for the competition in subsequent years. It is memorable not only because the problem is elegant but also from the personal connection with the person who was the only competitor to solve this problem completely during the competition. Though this was many years ago, I still remember him saying to me that the most important thing above all else is to keep your interests up. (Of course, he meant mathematics!) After all these years, I can proudly say that I have kept up my interest in the subject. Even though I am not a mathematician, mathematics is definitely an important part of my life. The sad part is that he is no longer with us but his words are as meaningful to me now as they were back then. In any case, here is the problem paraphrased in my own words:
Problem: There are 5 monkeys each standing at the bottom of 5 different ladders with a finite number of ropes tied between them. No rope is attached to the same rung of the same ladder. On the top of each ladder, there is a banana. Each monkey climbs up the ladder and must cross a rope when it comes across one. Once it crosses a rope, it must continue to go up the ladder. Prove that each monkey will get a different banana.
Many years later, there was a party in my condominium building. This problem was used to decide who gets certain prizes. Horizontal lines representing ropes were drawn between vertical lines representing ladders. Each household chooses the bottom of a ladder and the top of each ladder is a different prize. Obviously, I cannot resist thinking about this problem from the competition as the host traces the path leading to the prizes, and of course about him and the influence of his words in my life. I also wonder if anybody in the room knows how to prove that each household will get a different prize.
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