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By Stephen Ainley
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Extra info for Mathematical Puzzles
Sample text
44. D5S Shorter for Clancy The route shown in Fig. 45 has a length of 38, and only 11 turns. It is not the only pattern. [1 -, .... , D ...... r-"'I ...... , ...... C r"""I r r"""I Fig. 45 44 MA THEMA TICAL PUZZLES My best results for the same problem with different numbers of houses in a square are: Houses length turns 9 16 25 36 49 64 81 8 16 22 34 38 50 64 3 7 7 11 11 15 15 100 121 80 86 19 19 144 169 100 122 23 23 196 225 256 142 150 166 27 27 31 D6S Square cascades (I) 42 ways, (2) 24,024 ways.
E9 Slab and slablets Figure 51 shows a slab divided into 7 slablets of different sizes. In fact each of the 16 different dimensions, of slab and slablets, is a different whole number; so I call it a 'proper' slab. E 49 SHAPES AND SHAPES 11 19 15 let 7 ,1ft 13 :Ll 20 Fig. 51. What is the smallest possible proper slab? The number of slablets into which it is divided may be 7 or more or fewer, as you choose. By 'smallest' I mean smallest in area. E10 Acungulation An acungle, let us say, is a triangle with each of its angles smaller than a right angle.
See Fig. 20. My trip is thus (4 + (4J3/3)), or about 6'309, miles long, whether I go AXBCDA, ABXCDA, ABCDXA, or the reverse of any of these. B Fig. 20. c 24 B9S MA THEMA TICAL PUZZLES Fish-tanks round corners (l) 4 feet (2) 4 feet (3) 6 feet x 3 feet Fig. 21 illustrates the problem for rectangular (as well as square) tanks, and for a passage with two arms of possibly different widths. Consideration of the 5 similar triangles shows that (a) bl + pq= px + qy, and of course (b) p2 + q2 = 12. ~--x ----71 Fig.