By Henry E. Dudeney, Martin Gardner
For 2 many years, self-taught mathematician Henry E. Dudeney wrote a puzzle web page, "Perplexities," for The Strand Magazine. Martin Gardner, longtime editor of Scientific American's mathematical video games column, hailed Dudeney as "England's maximum maker of puzzles," unsurpassed within the volume and caliber of his innovations. This compilation of Dudeney's long-inaccessible demanding situations attests to the puzzle-maker's present for growing witty and compelling conundrums.
This treasury of interesting puzzles starts off with a range of arithmetical and algebraical difficulties, together with demanding situations related to cash, time, pace, and distance. Geometrical difficulties persist with, in addition to combinatorial and topological difficulties that function magic squares and stars, course and community puzzles, and map coloring puzzles. the gathering concludes with a chain of video game, domino, fit, and unclassified puzzles. recommendations for all 536 difficulties are incorporated, and fascinating drawings liven up the ebook.
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Additional resources for 536 Curious Problems and Puzzles
Indb 26 06/06/13 3:37 PM On the Number Line ◾ 27 asked around 1644 if one takes all the squares of the integers, computes the reciprocals, and adds them up, does one get a finite answer? In other words, he asked if the sum 1+ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 + + + + + + + + + + + + + + 4 9 16 25 36 49 64 81 100 121 144 169 196 225 is finite. The question was later referred to as the Basel Problem because several mathematicians from Basel gnawed at the problem, but without success. Among these were several members of the Bernoulli family, who resided in that Swiss city.
The “roughly” comes about because of the multiplication of three numbers, none of which is precise. If each is off by 10% from the proper value (which, after all, can easily happen), then the result can be too small or too large by more than 30%. However, in most cases one of the estimates will be too small, another will be too large, and the net result will be about right. For outdoor events, open-air concerts, or political rallies or demonstrations, such estimates are much harder to make. There are two reasons for this: first, the numbers are more difficult to estimate, and, second, there are vested interests (particularly for political events) in reporting impressively small or large attendance numbers.
The second sequence is one I generated on my computer using the computer algebra program Maple; and though these are not true random numbers but “pseudo random,” they should show no patterns even on a second look. The third sequence I simply wrote down by hand, so it may well show some patterns—even though I was very careful. Indeed, my careful effort to randomize may well have been a mistake. In fact, one can determine that numbers written down by hand always have too many regularities and noticeable problems—sufficiently many, and sufficiently idiosyncratic that one can even tell who wrote the sequence down.