A Mathematical Pandora's Box has been written in response to the success of Brian Bolt's earlier mathematical puzzle books. Through his own experience, the author has discovered a worldwide interest in these and similar puzzles. Not only do they stimulate creative thinking but they can also open up new areas of mathematics to the reader. This book contains 142 activities: in addition to puzzles, there are games, tricks, models and explanations of various phenomena. They range from number manipulation, through happy and amicable numbers, coin puzzles, picnicking bears and pentominoes, to building shapes with cubes. Some of the puzzles date from hundreds of years ago while many others are original, giving everyone something to think about. There is a detailed commentary at the end of the book, giving solutions and explanations, together with the occasional follow-up problem.

decreasing sequences of five numbers. 96 Fencing! Joe Appleyard wanted to build a fence to protect his orchard. The fence was to be built 90 m down one side of a valley and 78 m up the other side. The slope of the valley sides are shown, together with the heights of the valley sides above the valley's 54 m bottom. The fencing panels are 2 m long and 1.5 m high. How many panels will be needed? I 30 m 97 Triangular Nim Place 15 coins (or counters) to form a triangular array as shown. Two players

contortions! Surriya has 64 bricks. 64 = 8 x 8 = 4 x 4 x 4 Graham has 89 bricks. 89 = 8 x 8 + 4 x 4 + 3 x 3 =7x7+6x6+2x2 =8x8+5x5 84 32 Empty the glass! This puzzle can be quite frustrating, but satisfying to solve. 33 Mum's happy! The only number which is square, happy (see activity 29 for the definition of a happy number) and in an acceptable age range is 49. 34 A fascinating pentagonal array! 41 46 \ \ 51 (19)—22—63 \/_r-v 12—39—(68 )-74—42 4—29—34—7 78—47—52—3 85 35 Bending

fact that Rachel was the youngest daughter rules out the likelihood of her being 40, for her mother would then have been 16, so Rachel must be 24. The germ of the idea for this puzzle was given to me by Joe Gilks of Deakin University, Australia. 97 69 Which way to Birminster's spire? Birminster's spire is on a bearing of 018° from Ablethorpe's. The spires are in fact positioned at four of the vertices of a regular pentagon. Consider the diagram shown, based on the given information. Triangles

walks like those shown with six legs. There are a surprising number of these. Consider all such routes where the first two legs are of length 1 block. The third and fourth legs could be any length from 2 to 8, giving 7 x 7 walks. Keeping the first leg at 1 block, and increasing the second leg to 2 blocks, still leaves the third leg with 7 possible lengths, but reduces the fourth leg to a choice from 3 to 8 blocks, giving 7 x 6 further walks. By systematically increasing the second leg from 1 to

using only the integers from 1 to 10? 38 66 Fault-free rectangles — Imagine you have a large supply of 2 x 1 blocks (dominoes are ideal) and that you are investigating ways of fitting them together to make rectangles. For example, two ways of making a 5 x 4 rectangle are shown. But in each case there is what is known as a fault line in the pattern indicated by the dotted lines. These are straight lines corresponding to the edges of the blocks which cut right across the rectangle, and are