. Discovery. Science. discovi:ry 63 It should be pointed out that one may commence at any point in the series of operations by transferring the proper number of letters from one end to the other. Thus, suppose we choose to commence with the ninth direction of the first series, the new series of directions would be: rlrrrlllrlrlrr rlllr I, or if we commenced with (say) the eighth of the second series, the new series would run : rlrlllrrrlrlrlllrrrl. The particular direction we commence off with is fixed by the order of certain towns which we must visit initially. Suppose, for example, we are to
. Discovery. Science. discovi:ry 63 It should be pointed out that one may commence at any point in the series of operations by transferring the proper number of letters from one end to the other. Thus, suppose we choose to commence with the ninth direction of the first series, the new series of directions would be: rlrrrlllrlrlrr rlllr I, or if we commenced with (say) the eighth of the second series, the new series would run : rlrlllrrrlrlrlllrrrl. The particular direction we commence off with is fixed by the order of certain towns which we must visit initially. Suppose, for example, we are told to start at S (see the figure), proceed to H, then to J, then to E, then to D, and then to go once through all the other towns, and return to S. From S to H is either I or ;- depending upon whether we got to S from T or R. From H to J is r, J to E is i, E to D is r. Our directions initially are, therefore, either Mr or rrlr. The first of these combinations occurs in the First Series and the second in the Second. The solutions are, therefore, IrlrrrlllrIrlrrrlllr and rrlrlrlllrrrlrlrlllr, and the orders of the towns visited are respectively S, H, J, E, D, L, K, R, Q, M. N, C, B, F, G, U, .\,0, P,T,S and S, H, J, E, D, C, N, O, A, B, F, G, U, T, P, 0, M, L, K, R, S. Mr. Rouse Ball, who describes this game in detail, recommends the solver, for convenience and to prevent error, to make a mark at, or put down a counter on, each town as it is reached. A geometrical problem of a simpler and better-known kind is the " proof " by dissection that 65 = 64. If the square of side 8 in Fig. 2 be cut along the lines indicated, it may be fitted into a parallelogram whose sides are 13 and 5. The paradox depends upon the relation 5 X 13 - 8= = I and the fallacy lies in the fact that the four pieces of the cut-up square, when fitted together, do not really make a parallelogram. There is a small diamond- shaped space, the area of \yhich is i, which is apt to be overlooked unless the c
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