When I was a kid, one of my favorite movies was a Jim Henson
classic called Labyrinth
. It was a fun bit of fantasy starring a young Jennifer Connelly
as Sarah and David Bowie
as the crooning Goblin King. In particular there was a riddle in that movie I always liked because of its simple clever solution. I'm referring to the part when Sarah comes to a place in the maze where she must choose between two doors: one that leads to the castle, and one that leads to - certain death ~ dun-dun-DAH!
There were two guards - one who only spoke the truth and one who always lied - and she had just one chance to ask the right question and discern which door was which . . .
"What would he say if I asked him . . ?"
It's one of those riddles you memorize because deep down you secretly suspect that you might find yourself in a similar situation and would hate to be without that quick, potentially life-saving interrogative. For decades a tiny segment of my brain was devoted solely to preserving this snippet of arcane logic. So when I was greeted with the following riddle I was positively giddy with anticipation when I heard, "one who only tells the truth and one who always lies . . ." At last! I was a lion hiding in the tall grass - ready to pounce. I would wipe that smug smile off the face of my foolish inquisitor (which happened to be a computer, but it was
being smug.) How dare it challenge me with such a simple riddle! But then I heard the rest of the riddle and my euphoria swirled into surprise and confusion.
"I know this one! . . . I, uh . . . just gimmie a sec . . . um . . . lemme get out some paper. . ."
And here I am, twelve hours later, finally victorious yet still unable to sleep. After wrestling with this puzzle all day I feel I need to pass it along before I can let go of it. So here is my version of what is perhaps the hardest riddle I've ever solved:
In the old temple are three great oracles who can divine the answer to any question. One of the oracles always speaks the truth, one always lies, and the third spouts only random nonsense. Because they are truly great oracles, they understand any language, but being the esoteric mystics they are, they choose to answer questions only in their own inscrutable language. When asked questions they always reply with ‘ja’ or ‘da’ - meaning either ‘yes’ or ‘no’, but nobody knows which means ‘yes’ and which means ‘no’. Whenever a petitioner asks a question he or she must choose an oracle to address and only that oracle responds. Even worse, each petitioner may not ask more than three questions in total. The challenge is to identify which oracle is which. Hints
I recognized two major obstacles to solving this puzzle: 1) the Random oracle, and 2) not knowing ‘yes’ from ‘no’. Fortunately for me, my intuitive sense that this puzzle would be solved in much the same way as Sarah had chosen her door in Labyrinth was correct. The key (for me at least) was using counterfactuals to elicit meaning from the responses. (I was surprised to discover there are several valid methods to solving this puzzle - but more on that later.)
I felt I could handle the puzzle if I could eliminate the Random element so I focused on creating a question that would isolate it so I could avoid it. I thought this was going to be very complicated because I also didn’t know ‘yes’ from ‘no’, but I kept messing around with different ways of phrasing the question. My breakthrough finally came when I reflected on the original Labyrinth puzzle and realized that even though you can discern the ‘truth’ of questions posed, you never know – and you needn’t ever know – which guard is actually truthful. Could I similarly elicit meaning from a response without ever needing to know if ‘ja’ meant ‘yes’ or ‘no’?
My first question (to the first oracle) is:
“If I asked you, ''Does the second oracle give random answers?'', would you say ‘ja’?”
This is a heavy question with heavy implications. Take some time to ponder all its possible outcomes and the total solution to this puzzle will likely become clear.