. Most people will say at once, the former ; but they are wrong. For with the first choice the man would receive £400 in the first year, and with the second choice £200 + £210. He has thus £10 more at the end of his first year. During the second year his first choice would give him £440, his second choice £220 + £230. Again he has £10 more, and this continues each year. Geometrical recreations consist chiefly of fallacies, paradoxes, and games of position, and it will be sufficient for me to illustrate them by taking a typical example of the latter known as the Hamiltonian Game.* ' W. W. Rouse
. Most people will say at once, the former ; but they are wrong. For with the first choice the man would receive £400 in the first year, and with the second choice £200 + £210. He has thus £10 more at the end of his first year. During the second year his first choice would give him £440, his second choice £220 + £230. Again he has £10 more, and this continues each year. Geometrical recreations consist chiefly of fallacies, paradoxes, and games of position, and it will be sufficient for me to illustrate them by taking a typical example of the latter known as the Hamiltonian Game.* ' W. W. Rouse Ball in Malhcmatical liecrealioiis, 1919, p. 189. This game was invented by Sir William Hamilton, and consists in the determination of a route along the edges of a regular dodecahedron which will pass once and once only through every angular point. As a dodecahedron is a solid figure, it is consequently difficult to use for this game, and for the purposes of solution the solid may be conveniently represented by either of the diagrams of Fig. i. To make the problem really a game, Hamilton gave each point lettered in the diagram the name of a town, so that the game consists in starting at any town and going " all round the world," visiting every town once only, and ending up at the point of departure. The game is varied by compelling the solver to visit certain towns in a certain order first before going on to the others. Not more than five towns should be included in this restriction. The problem is attacked in the following way: At each angular point there are three edges (three lines in the diagram). As we approach a point there are only two routes open to us after passing it—the one leading to the right is denoted by r, that to the left by I. If we go to the left; then, after passing a town, to the right; then, after passing a second town, to the left, we denote the operation bj' Irl; twice to the left and once to the right by l-r, and so on. Five times i
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