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By Brian Bolt

131 actions, starting from matchstick and coin puzzles via ferrying, railway shunting, dissection, topological and domino difficulties to a number of magical quantity arrays with wonderful homes are integrated.

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131 actions, starting from matchstick and coin puzzles via ferrying, railway shunting, dissection, topological and domino difficulties to a number of magical quantity arrays with dazzling houses are integrated.

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12. There are only two solutions. 84 About turn! Three-digit numbers exist so that abc x def = ghijk and cba x fed = kjihg are both true at the same time, such as 131 x 111 = 14541 and 102 x 201 = 20502 But these rely on a degree of symmetry to work. What is remarkable, however, is that such numbers exist which exhibit no symmetry. Can you find any of them? 44 85 Quadrilles 1 6 1 1 i 2 2 JL 1 6 1 6 1 1 2 2 3 6 5 5 4 4 3 L 5 4 5 I I I I I I I 3 3 4 i Select the appropriate twelve dominoes from a standard double-six set to make up the pattern shown.

What were the ages of the Rev. Pascal and his wife on their wedding day? 24 9 22 © 18 20 33 19 29 1 14 0 v) (39) 25 35 2 12 26 © 16 50 Envelopes of curves 34 To envelope', the dictionary tells us, is 'to wrap up' or 'to 31 surround'. We use an 30 envelope to put a letter or 29 card in before sending it through the post, and mathematicians use the word when they have a family of lines (or other curves) which surround a shape. In the drawing the lines seem to form a circle, although the 22 circle itself is not drawn, and are said to be an envelope.

43 83 Star puzzle 2 The numbers 1, 3, 5, 7, 9, 11, 10, 12, 13, 14, 15, 17, have been arranged in the six-pointed star so that the totals of the five numbers along each of the six lines indicated are all equal to 45. Magic! The challenge for you is to create a similar magic star using the numbers 1, 2, 3, 4, . . , 12. There are only two solutions. 84 About turn! Three-digit numbers exist so that abc x def = ghijk and cba x fed = kjihg are both true at the same time, such as 131 x 111 = 14541 and 102 x 201 = 20502 But these rely on a degree of symmetry to work.

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