Each issue Jerry, O4R's puzzle guy, brings you a set of puzzles. As always, the answers will be published in the next issue. They are now posted here as well! Questions and discussion may be directed to Jerry.
PROBLEM 1 Nat, the neat nephew, has two aunts, Nelly and Nancy. One lives at each end of a bus line. Nat visits each aunt on alternate Sundays. He notices that sometimes when he visits Nelly the first bus is going the other way, and symmetrically when he visits Nancy. A little research establishes that a bus leaves either terminus at 10-minute intervals and they travel the same speed. (For simplicity, assume the stop time at each station is zero.) So Nat the nathenatician decides to arrive at the station at random times, realizing, of course, that he may visit the same aunt on more than one consecutive Sunday. But, allowing for an infinite set of Sundays, it will all average out. (The Law of Large Numbers seems to support this common sense reasoning.) But, alas and alak, he finds that 80% of his visiting is with Nelly and only 20% with Nancy. This can happen in two different ways. What are they? [HINT: In actual practice, i.e. everyday life, it works this way, maybe 70-30, 43-57, or 23.89-77.11, but not likely 50-50.]
PROBLEM 2 Hang a half-full pail of milk from the ceiling (way up there). The milk and pail are at rest with each other. Notice how the milk sits "flat" in the pail. Now wind-up the string, let go and watch the pail spin. Friction causes the milk to begin to spin also and, after awhile, the milk and pail are once again essentially at rest with each other. But now there's a great big meniscus in the center of the milk.
Newton proposed this experiment as a demonstration that space was absolute (not relative, as the Theory of Relativity demands). So what's wrong? Ernst Mach said the situations were different because the fixed stars were at rest with respect to the first case and not with the second. The only way to prove it is to go up there and rotate the fixed stars so they are at rest with the pail with the meniscus. Is there a better (less "out there") answer than this? If you have one, email it to me and we'll put it in the next issue.
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