The “Ladder Problem”
Monte J. Zerger · Mathematics Magazine · 1987
A good mathematical problem is like a good song. It keeps coming back time and time again. And just as a song, when it comes back periodically, is still the same song-just sung by someone new in a different style-so a problem often reappears to be proposed in a different framework and/or solved in a different way. Such is the case of the problem I have come to call, affectionately, the ladder This problem was originally posed to me by an engineer who said it was being kicked around in various engineering circles. I don't know its original source; it may be lost in antiquity. Before I pose the I would like to ask, What is a 'good' problem? Of course, that is open to numerous opinions, but surely it would meet several of the criteria listed below and, perhaps, these criteria could be used in evaluating candidates. 1. It can be described quite simply and the crux of the problem can be quickly grasped by one with even minimal mathematical background. 2. It can be nicely cast in a physical, tangible framework. 3. It immediately intrigues and challenges people to whom it is posed. 4. It can be solved in a creative, refreshing and elegant manner, as well as in, perhaps, a more straightforward, but uninteresting way. 5. It can be solved in a variety of ways. 6. It can be solved without using higher mathematics. 7. It quickly suggests a variation or generalization which results in an even more challenging problem. The ladder problem, I believe, excels in all these categories. Here is the problem as it was posed to me: