The Counterfeit Coin Problem

Extract

There is a problem which is much in favour at present of which one version is this : a man has 12 pennies among which there may be a counterfeit coin, which can only be told apart by its weight being different from the others. How can one tell in not more than three weighings whether there is a counterfeit penny, if so which one it is, and whether it is heavier or lighter than a normal penny? (Math. Gaz., XXIX (1945), pp. 227–229; XXX (1946), pp. 231–234.) This puzzle seems to have originated in America. The purpose of the present note is to make clear what is the best possible solution in the most general case of any version of the problem. No originality is claimed for these solutions, as no doubt many of them have been obtained independently many times before : but I am not aware that any complete and systematic account has yet been published.