Are you itching to test your smarts? You’ve come to the right place. The Harvard Business Review may have published this logic puzzle back in 1996, but people are still scratching their heads over it today. (If you prefer numbers over words, find the missing one in this puzzle.)
Mathematician Richard Smullyan, nicknamed “the undisputed master of logical puzzles” by former PhD student Bruce Horowitz, really outdid himself with this brainteaser. As a matter of fact, Smullyan’s colleague, an MIT logic professor named George Boolos, called it “the Hardest Logic Puzzle Ever”—and we can see why.
Here is the riddle, straight from the mathematician’s mouth: “Three gods, A, B, and C, are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is completely random. You must determine the identities of A, B, and C by asking three yes-or-no questions, and each question must be posed to exactly one god. The gods understand English, but will answer all questions in their own language. In their unknown language, the words for “yes” and “no” are “da” and “ja,” in some order. You do not know which word means which.”
So, which questions would you ask to identify each god? And no, it’s not a trick question. As a matter of fact, there are multiple ways to get the correct answer.
We’re willing to bet that your brain feels pretty busted at this point. If you’re ready to throw in the towel and hear the solution, we won’t tell! Here are the three questions you should ask, according to Nautilus:
1. To god A: “Does ‘da’ mean ‘yes’ if and only if you are True and if and only if B is Random?” (We supposed A said, “ja,” making B True or False).
2. To god B: “Does “da” mean ‘yes’ if and only if Pluto is a dwarf planet?” (We supposed B said, “da,” making B True.)
3. And to god B (True) again: “Does ‘da’ mean ‘yes’ if and only if A is Random?” Since B’s True, he must say “da,” which means A is Random, leaving C to be False.
Don’t beat yourself up if you’re still a little confused. You can start sorting out the solution with this 2008 paper, which claims to have the easiest answer to the brainteaser. But if you’d rather give your brain a break (and test your visionary skills, instead!) find out how many triangles are in this image. Or, better yet, see if you can spot the difference in these 10 pictures. Good luck!