Puzzle #11: Smullyan’s Truth Machines
A magic store sells truth-telling machines. The machines each have a yellow light and a blue light that illuminate in response to true-or-false questions, with one light corresponding to “true” and the other to “false.” The store owner has three machines. She tells you that two of them work and tell the truth, but one of them is broken and outputs random answers. She doesn’t know which one is broken. Furthermore, she doesn’t know which light colors correspond to true and false, and the meaning of the lights might differ between machines (i.e., in one machine a yellow light might mean “true,” while in another machine a yellow light might mean “false”). Ask a single true-or-false question to one machine to guarantee that you walk away with a functioning truth-telling machine.
Machines that answer randomly are considerably harder to wrangle than knaves who always lie. Consistent liars mislead in predictable ways! Not knowing what the lights mean and that they can differ across machines poses even more obstacles. While this puzzle is not for the faint of heart, determined mortals can solve it.
Find the solution at the bottom of this page.
