By Raymond M. Smullyan
A number puzzles facing notice play and common sense, arithmetic and philosophy, that includes Alice and the creatures of Wonderland
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Extra resources for Alice in puzzle-land : a Carrollian tale for children under eighty
7. 128 INCHES T B L Let H represent the head, B the body, T the tail, and L the total length of the fish. Looking at the problem we are given the following three facts: T= H+ 1B B3=L H = 4 inches It is also true that L = H + B + T H 41 In this equation keep L and substitute for everything else. WL = 8 inches L = 8 X 16inches L = 128 inches Thus we see that the fish was 128 inches long. 4. Are You at Home in Rome? 1. THE ABACUS The merchants and traders of ancient days in Egypt and Mesopotamia used to set out pebbles in grooves of sand to calculate and add up accounts.
191 15. Letters for Numerals 1. X=9,Y=1,Z=8 Examine the units column. X + Y + Z = 10 + Z, which means that X + Y = 10. Examine the tens column. X + Y + Z + 1 (from the units column) = lO + X, which means that Y + Z = 9. Examine the ten-thousands column and the equation obtained is: X + Y + Z + 1 (from the thousands column) = lOY + X. Substitute Y + Z = 9, and the equation then becomes: 10 = lOY, or Y = 1. From this it follows that Z = 8, and X = 9. 9999 1111 8888 19998 2. X=5,N=2,P=l,S=O,R=6,andZ=3 Examine the second row of multiplication by X.
The lengths of the sides of the parallelogram are varied to produce the different sizes of the copy. The original and the copy are in two dimensions and lie in the same plane. 52 6. FALSE A histogram is in no way connected with the unit of weight, the gram. It is true that the metric standards are kept at the International Bureau of Weights and Measures at Sevres near Paris. The histogram is connected with the method of graphical representation of data, and is described elsewhere in this book. 7.