English

HAKMEM

MIT AI Memo 239 (February 1972). A legendary collection of neat mathematical and programming hacks contributed by many people at MIT and elsewhere. (The title of the memo really is “HAKMEM”, which is a 6-letterism for ‘hacks memo’.) Some of them are very useful techniques, powerful theorems, or interesting unsolved problems, but most fall into the category of mathematical and computer trivia. Here is a sampling of the entries (with authors), slightly paraphrased: Item 41 (Gene Salamin): There are exactly 23,000 prime numbers less than 218. Item 46 (Rich Schroeppel): The most probable suit distribution in bridge hands is 4-4-3-2, as compared to 4-3-3-3, which is the most evenly distributed. This is because the world likes to have unequal numbers: a thermodynamic effect saying things will not be in the state of lowest energy, but in the state of lowest disordered energy. Item 81 (Rich Schroeppel): Count the magic squares of order 5 (that is, all the 5-by-5 arrangements of the numbers from 1 to 25 such that all rows, columns, and diagonals add up to the same number). There are about 320 million, not counting those that differ only by rotation and reflection. Item 154 (Bill Gosper): Th

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