By Henry E. Dudeney
Virtually each kind of mathematical or logical poser is incorporated during this outstanding assortment — difficulties in regards to the manipulation of numbers; unicursal and path difficulties; relocating counter puzzles; locomotion and pace difficulties; measuring, weighing, and packing difficulties; clock puzzles; mix and workforce difficulties. Greek move puzzles, difficulties regarding the dissection or superimposition of airplane figures, issues and features difficulties, joiner's difficulties, and crossing river difficulties significantly try 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 provides you with an unparalled chance to workout your logical, in addition to your mathematical agility.
Each challenge is gifted with Dudeney's precise 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. many of the difficulties are unique creations — yet Dudeney has additionally incorporated many age-old puzzlers for which he has stumbled on new, astonishing, and typically less complicated, solutions.
"Not purely an entertainment yet a revelation … "— THE SPECTATOR.
"The top miscellaneous number of the type …"— NATURE.
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Extra resources for Amusements in mathematics
Illustration: FIG. ] [Illustration: FIG. ] I will now explain, as I promised, why a Greek cross may be cut into four pieces in an infinite number of different ways to make a square. Draw a cross, as in Fig. 16. Then draw on transparent paper the square shown in Fig. 17, taking care that the distance c to d is exactly the same as the distance a to b in the cross. Now place the transparent paper over the cross and slide it about into different positions, only be very careful always to keep the square at the same angle to the cross as shown, where a b is parallel to c d.
1 into three pieces that will fit together and form a half−square triangle. The answer that is invariably given is that shown in Figs. 1 and 2. " But no serious puzzle lover will ever admit this. If the cut is made so as to leave the four pieces joined in one, then it cannot result in a perfectly exact solution. If, on the other hand, the solution is to be exact, then there will be four pieces−−or six pieces in all. It is, therefore, not a solution in three pieces. [Illustration: Fig. 1] [Illustration: Fig.
Therefore we know that the square of DF will contain the same area as the cross. This fact we have proved practically by the solutions of the earlier puzzles of this series. But whatever length we give to DE and EF, we can never give the exact length of DF in numbers, because the triangle is not a "rational" one. But the law is none the less geometrically true. [Illustration: FIG. ] [Illustration: FIG. ] Now look at Fig. 29, and you will see an elegant method for cutting a piece of wood of the shape of two squares (of any relative dimensions) into three pieces that will fit together and form a single square.