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 remarkable houses are incorporated.
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Extra resources for Mathematical Cavalcade
98 Self motivated! A*/". V Judy and Nigel were keen to get to a pop festival at a town 21 miles away, but having missed the bus they would have to make their own way. Judy was a keen cyclist and could speed along on her cycle at 16 mph. Nigel didn't own a cycle, but reckoned he could average 12 mph on Judy's cycle. Judy can jog at 6 mph quite happily, while Nigel considers himself a runner and can jog at 8 mph for many a mile. How should they arrange their journey so that they leave home together and arrive at the festival together in the shortest possible time, by a mixture of jogging and sharing the bicycle?
One more counter of a different colour or size can then be used for the fox who starts at the square marked F, in the centre. The geese can move one square at a time either left, right or down but not up or diagonally. The fox can move one cell at a time either left, right, up or down. Further, it can jump over a goose (and remove it), if the goose is in its path and the square on the other side of the goose is vacant. The object of the game is for the geese to surround the fox so that it cannot move, while the fox tries to consume the geese and avoid capture.
Continue this halving and doubling process until the last number in the left column is 1. Finally, add together all those numbers in the right-hand column which come opposite an odd number in the left-hand column (shown arrowed). The sum of these numbers gives the required product: 39 x 79 = 79 + 158 + 316 + 2528 = 3081 Try out this method for yourself on other numbers and check the correctness of the product using a calculator or other means. Can you explain why the method works? 110 Crossed ladders In an alleyway between two houses two ladders are leaning against the walls as shown.