13.1 Algebra Comes Out to Play

For two years we have leaned on algebra to describe situations, untangle equations, and pin down the values of unknown letter-numbers. So far the work has been earnest. Time to lighten up. Here we will poke at tricks and puzzles, use algebra to explain why each one works, and, the best part, figure out how to cook up fresh ones to dazzle our friends.

One idea threads through the whole chapter: a letter-number can represent “any number you happen to pick,” and algebra then reports exactly what becomes of it, regardless of which number that was. When a trick lands on the same answer for one starting value and again for another, that is no coincidence; it is algebra wearing a disguise.

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