Chapter 12: Calculating for Fun

Getting students to carry out calculations can be difficult unless one embeds the calculations in an amusing or interesting setting. This chapter describes several calculations which have intrigued students for centuries and ought to intrigue students for centuries to come. This leads to large numbers and the interest of the problem is to make these numbers comprehensible. The problems include: the chessboard problem; the landowner’s earth and air problem; the value of Manhattan Island; heavy rainfall; permutations of the alphabet and the number of crosswords; grains of sand versus stars in the sky; winning the lottery versus dying; the size of a million pounds. Each of these leads to large numbers and the interest of the problem is to make these numbers comprehensible. In addition, the problems lead to questions of measurement, area, volume, the size and population of the earth, interest rates, etc., and some research may be needed to determine the relevant numbers. Each student or group can be encouraged to produce improved measurements, variations on the method or variations on the problem itself. As a further variation, one can convert into other systems of units — in first year physics, we had to convert the speed of light into furlongs per fortnight.