101 Mathematical Projects by Brian Bolt, David Hobbs

By Brian Bolt, David Hobbs

This ebook for lecturers indicates initiatives which cater for quite a lot of options and talents, and hyperlinks with different curriculum matters.

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At each turn a player must take at least one match but not more than 4 matches. The player who takes the last match wins. In this game there can be more than one pile and any number of matches in each pile, for example, 3, 4, 5. • (a) A strategy can be found by working 'backwards': in order to win you must leave your opponent 5 matches so that if they take 1 or 2 or 3 or 4 matches you take 4 or 3 or 2 or 1. In the same way it can be seen that at the previous stage you must leave 10 matches. Thus certain key numbers can be deduced.

2 A marble maze The customer pays lOp a time to drop a marble in at the top of the board. The board can be made from plywood. The distances between the nails depend on the diameter of the marbles. The channels at the bottom can be made by glueing strips of wood to the board. / I h I I I \ Games and amusements 47 The game can be analysed by considering the theoretical outcomes of dropping 32 marbles in at the top. With the scheme shown this gives a profit of 60p every 32 games. 32 vwv vwwv 2 « 8 « 1 2 « 8 * 2 * \ / \ / \ / \ / \ Try the game out as in the last paragraph of 1 above.

Find the level of performance in each event which corresponds to 1000 points. How many points would the current world records in these events be worth? What were the individual performances which Daley Thompson achieved to get the world decathlon record? What did they each score in points? Daley's personal goal is to exceed 9000 points. Which discipline shows most room for improvement? How did Judy achieve her Commonwealth record in 1986? ), Athletics: the International Track and Field Annual (Simon and Schuster) IAAF, Scoring Tables for Men's and Women's Combined Event Competitions (International Amateur Athletic Federation) D.

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