This is a very tantalizing puzzle from one of the Martin Gardner books “More Mathematical Puzzles and Diversions” (Chapter 14, Puzzle #4).
When Professor Stanislaw Slapenarski, the Polish mathematician, walked very slowly down the down-moving escalator, he reached the bottom after taking 50 steps. As an experiment, he ran up the same escalator, one step at a time reaching the top after taking 125 steps.
Assuming that the professor went up five times as fast as he went down (e.g., took five steps to every one step before), and that he made each trip at a constant speed, how many steps would be visible if the escalator stopped running?
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Happy up & down the escalator!