A Mathematicians Miscellany by JE Littlewood

By JE Littlewood

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Of forms (one of them letters in wrong envelopes a number the latest is as the source of the sub -factorial notation) From two shuffled packs the two top cards are turned up, then the next two, and so on. g. both is ; follows. known, but most people good odds against actually 17 10 on (practically e1 I). odds are approximately the In the other we have a group of 23 people what are the odds that some pair of them have the same birthday ? l Most people will say the event is unlikely, actually the odds 7's of spades).

1 I ought to write , but here courage fails me. A MATHEMATICIAN'S 52 I 20. MISCELLANY do not deny that the example just given is slightly a more respectable one. For any disreputable of a property trajectory in an atmosphere of varying the density, say property of having range R for given 1 elevation (and fixed gun ), there is an equivalent homogeneous atmosphere (in which the E for the given it varies of course is the same as in the actual atmosphere with <) this is expressed by a fraction c, the equivalent constant density being that at height ch, where h is the greatest height in the trajectory.

MISCELLANY do not deny that the example just given is slightly a more respectable one. For any disreputable of a property trajectory in an atmosphere of varying the density, say property of having range R for given 1 elevation (and fixed gun ), there is an equivalent homogeneous atmosphere (in which the E for the given it varies of course is the same as in the actual atmosphere with <) this is expressed by a fraction c, the equivalent constant density being that at height ch, where h is the greatest height in the trajectory.

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