Download e-book for iPad: Amusements in mathematics by Henry E. Dudeney
By Henry E. Dudeney
Virtually each type of mathematical or logical poser is incorporated during this outstanding assortment — difficulties about the manipulation of numbers; unicursal and path difficulties; relocating counter puzzles; locomotion and velocity difficulties; measuring, weighing, and packing difficulties; clock puzzles; blend and team difficulties. Greek pass puzzles, difficulties concerning the dissection or superimposition of airplane figures, issues and contours difficulties, joiner's difficulties, and crossing river difficulties significantly try out the geometrical and topological mind's eye. Chessboard difficulties, regarding the dissection of the board or the location or circulate of items, age and kinship problems, algebraical and numerical difficulties, magic squares and strips, mazes, puzzle video games, and difficulties bearing on video games provide you with an unparalled chance to workout your logical, in addition to your mathematical agility.
Each challenge is gifted with Dudeney's exact urbane wit and sense of paradox, and every is supplied with a clearly-written answer — and sometimes with an fun and instructive dialogue of the way others attempted to assault it and failed. lots of the difficulties are unique creations — yet Dudeney has additionally incorporated many age-old puzzlers for which he has found new, mind-blowing, and typically less complicated, solutions.
"Not simply an entertainment yet a revelation … "— THE SPECTATOR.
"The most sensible miscellaneous selection of the type …"— NATURE.
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Extra resources for Amusements in mathematics
Illustration: Fig. 6] [Illustration: Fig. 7] [Illustration: Fig. 8] [Illustration: Fig. 9] [Illustration: Fig. 10] [Illustration: Fig. 11] It will be seen that every one of these puzzles has its reverse puzzle−−to cut a square into pieces to form a Greek cross. But as a square has not so many angles as the cross, it is not always equally easy to discover the true directions of the cuts. Yet in the case of the examples given, I will leave the reader to determine their direction for himself, as they are rather obvious from the diagrams.
This got accidentally torn in half, so that 3 0 was on one piece and 2 5 on the other, as shown on the illustration. On looking at these pieces I began to make a calculation, scarcely conscious of what I was doing, when I discovered this little peculiarity. If we add the 3 0 and the 2 5 together and square the sum we get as the result the complete original number on the label! Thus, 30 added to 25 is 55, and 55 multiplied by 55 is 3025. Curious, is it not? Now, the puzzle is to find another number, composed of four figures, all different, which may be divided in Amusements in Mathematics 32 the middle and produce the same result.
Illustration: FIG. ] [Illustration: FIG. ] It will be seen that 9 added to 16 equals 25, the number of cells in the large square. If you make triangles with the sides 5, 12 and 13, or with 8, 15 and 17, you will get similar arithmetical proofs, for these are all "rational" right−angled triangles, but the law is equally true for all cases. Supposing we cut off the lower arm of a Greek cross and place it to the left of the upper arm, as in Fig. 28, then the square on EF added to the square on DE exactly equals a square on DF.