Question

It is given {eq}12

{/eq} balls, all equal in weight except for one that is either heavier or lighter. Also it is given a two-pan balance to use. In each case, use of the balance you may put any number of the {eq}12

{/eq} balls on the left pan, and the same number on the right pan, and push a button to initiate {eq}1

{/eq} the weighing; there are three possible outcomes: either