The Games and Puzzles Journal, #8+9 - Mayhematics

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page L22 THE GAMES AND PUZZLES JOURNAL issue 8+ 9 DISSECflONS There are four pages of Dissections in this double issue - mainly on polyominoes. I hope my request for some original results on p.124, and Mr Mabeyrs beautiful results on p.125 will lead to further work, so that we can revive the FCR tradition of publishing a regular series of problems. We have the advantage nowadays of being able to illustrate the results without resorting to coding. Pentomrnoes Here are the solutions to Sivy FARHI|s dissection problems on pages 5? and 109, and six further cases he has found. He evidently has the whole problem computerised. In each of these configurations, given the positions of the four holes and the 1xb piece the positions of the other 11 pentominoes are determined uniquely. W rWW lwbt- t;I H =ti L-', L'l ,_L__-l fuL) 7JZI i---f r -J r-- .!l w:_ Solutions to the Geometri,c Jtgscws three probtems posed last time are as follows: (c) edge and corner Pieces only (a) omitting the two square-sym metric pieces I L---\ NJ I +- (b) omitting the square-symmetric pieces and the standard Piece Michael Keller sent solutions of these. His results all differ from mine - the solutions are not unique. Len Gordon comments that rGeometric Jigsaws' appear in MaJor Percy Alexander MacMahonts 1921 book New Mathematical Pastimes. (Cambridge University Press). However, he did not consider shapes with bobbles and nibbles, and his selections of tiles to fit together are based on combinatorial rather than geometrical considerations.
issue 8+9 THE GAMES AND PUZZLES JOURNAL A $rperDomino Twtgram By Leonard J.GORDON . The second part of MacMahonrs book, New Mathernatiqal pastimes, I1ZI, togeometricaltransformationsofthecolouree'osi and simple transformations are made with the square 3-colour super-dominoes, using 2-to-3 contact system. One such set of transformations is: x"[x'DX*K K-?w-7 page I23 is devoted interest i ng the 1-to- 1 n Noting that a tile with two adJacent 2ts or two adJacent 3's produced a side angled ht 45o' it was interesting to speculate if a practical 'tangramr eould be produced in this way. The idea was to select a set of pieces to produce the best tangram, rather than use MacMahon's normal selection process. Here is how one tangram was found. Arrange square super-dominoes with the 2 and 3 compartments as in diagram A. This produces a tilted rectangular shape when transformed. Thenr chbose colours for the other compartments so as to satiify the contact rules, and also to have enough of colour L to allow forming a rectangle with an all colour 1 border. Also, choose the colours so all 12 pieces are different. Diagrams B and C show one set of tiles which satisfy these requirements. This 3x4 units rectangle can be rearranged to a 2^/2xB:/2 rectangle correspoltding to the first diagram, A. B A second interesting tangram was made by transforming the tiles shown in diagram D, Two each of these six tiles allo form either of the two above rectangles. A typical problem with the second set is to form the two crosses, as in diagram E. In addition, either set allows for the fancifuf designs made with the more common tangrams. ,XKK N"fi KKK u 1__r With the first set, the Editor notes that it is possible to form a square 5VZxl\/2 with central hole t/Zx\/Z as in F.
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