ABSTRACT
This chapter exhibits the power of simple algebra, where values of interest are treated as variables and knowledge about them is coded as equations. Thirteen puzzles and a theorem are used to show this power; among them are conundrums about prices, runners, rectangles, round-robin competition, lily-pad hopping, dice design, and strategy for buying lottery tickets.
In this last case, the reader is asked to imagine that he or she has come along just as a church lottery is closing; its prize is a quilt worth $100 to the reader, and only 25 tickets have been sold.
At $1 a ticket, how many tickets should the reader buy? The theorem at the end of the chapter tackles the classical problem of computing the probability that a family name will die out, given the probability distribution of name-bearing children for each family member.
