Mathematical recreations and essays . ^ ^^H^WW ^ ^^^^^^^ ^ ^ ^^^F^ ^ A ?Z^ ^ C^ ^ ^3 p p^ P f ^mj L t^ ^ ^ SA k, 773^ 5^ ^ A ^A p k^ w Examples of Tesselated Pavements. If more than two colours are used, the problems becomeincreasingly difficult. As a simple instance take sixteen squaretiles, the upper half of each being yellow, red, pink, or blue,and the lower half being gold, green, black, or white, no twotiles being coloured alike. Such tiles can be arranged in theform of a square so that in each vertical, horizontal, and diagonalline there shall be 8 colours and no more; or so that theresh
Mathematical recreations and essays . ^ ^^H^WW ^ ^^^^^^^ ^ ^ ^^^F^ ^ A ?Z^ ^ C^ ^ ^3 p p^ P f ^mj L t^ ^ ^ SA k, 773^ 5^ ^ A ^A p k^ w Examples of Tesselated Pavements. If more than two colours are used, the problems becomeincreasingly difficult. As a simple instance take sixteen squaretiles, the upper half of each being yellow, red, pink, or blue,and the lower half being gold, green, black, or white, no twotiles being coloured alike. Such tiles can be arranged in theform of a square so that in each vertical, horizontal, and diagonalline there shall be 8 colours and no more; or so that thereshall be 6 colours and no more; or 5 colours and no more;or 4 colours and no more. Colour-Cube Problem. As an example of a recreationanalogous to tesselation I will mention the colour-cube of mathematical technicalities the problem maybe enunciated as follows. A cube has six faces, and if sixcolours are chosen we can paint each face with a differentcolour. By permuting the order of the colours we can obtain * On thi
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