the three crosses

My grandfather loved word puzzles, logic riddles.

When I was thirteen or so he attempted to teach my brother and I how to play blackjack.  I can remember sitting at a table writing down the things he told me (no doubt he suggested I go grab a pen and paper to commit his “system” to memory).  He’d deal hand after hand of twenty-one to each of us, bloody mary or whiskey neat not far out of reach, and instruct as we played.

It’s a pity I didn’t understand how important those interactions were.  What stories.  He told us of gambling on a riverboat on the Mississippi. This is the same grandfather that bought me a .22 rifle when I turned twelve and used to send me handwritten missives address in my last name prefixed by the regal-sounding “Master.”  Do you know how cool it was to get a letter like that as a kid?  He was a character.

Between explaining the concepts of insurance and splitting and doubling and when to hit and when to hold he would regale my brother and I with his riddles.  Most you’ve probably heard: the fox, the goose, and the sack of wheat; the liar and the truthteller; the hotelier and the three magicians.  But my grandfather’s coup de grĂ¢ce was a puzzle he called “the three crosses.”  I can recall him building up to this one, happy that my brother and I were truly trying to puzzle out the lead-in problems.  It went something like this:

Three men go into an office, all to interview for the same job.  The employer takes all three into a room at together and explains that this position requires a keen intellect and solid sense of reason, and that they’ll all be put to the test for their interview.

The interviewer arranges three chairs in a triangular formation and seats each man in a chair so that each can see the other two.  He then blindfolds each man and explains aloud that he will be using chalk to draw either a white or black cross on each man’s forehead.

Unbeknownst to the men the employer draws black crosses on each of them.

He then instructs them to remove their blindfolds and to knock on their chair if they see at least one black cross.  Furthermore, he states that the first man to correctly identify the color of the cross drawn on his own forehead, and explain correctly why he is sure of this, will secure the position.

The men lift their blindfolds together and all three begin rapping on their chairs.  Thirty seconds elapse and one man raises his hand to announce that he surely has a black cross on his forehead.

How did he know?

At thirteen this riddle wrecked my brain.  No there are no mirrors; no he didn’t catch a reflection in another’s eye; no he didn’t cheat and smudge his hand against his skin.  I can vividly recall sketching out the triangle, trying to grasp the situation.  My brother and I even acted out the scenario with the help of my grandfather.  He was beyond amused at how hard we thought on that puzzle, and remarked accordingly, “Boy David you’re really thinking hard on this one, good!”  To him the mental exercise was the fun (I suppose with him for a grandfather and my dad for a father I was doomed to a similar stuffy intellectual sentiment).

Try as we might, however, my brother and I could simply not crack the puzzle.  I think what frustrated me more, though, was being unable to understand the answer when my grandfather finally deigned to accept our defeat and explain it.  I asked him to go through it over again for me, talk through the steps really slow so I could get it.  It didn’t work.  I would think I understood and then try and follow the logic in my own head and get confused.  Thinking on the answer now it’s clear enough, but back then it may have been a bit beyond my grasp.  It’s one of the clearest and fondest memories I have of my grandfather though… and for that I’ll always remember  it.

Before I go, I wanted to show you Cohen’s new smile.

And that’s mild compared to some of the ones we’ve not had the presence of mind to capture on video.


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8 Replies to “the three crosses”

  1. you really sparked a lot of memories for me with this one. I literally grew up having to figure these things out constantly and usually received the tongue lashing because I couldn’t. I don’t even remember the solution for the three crosses after all these years. You’d think as many times as I had it drummed into me it would never have left. Selective retention? maybe

  2. Dying of curiosity and not wanting to puzzle the solution for myself, I tried to google for the right answer… Top google result for “Three crosses logic problem”? This post.

    Boo Dave, boo. I guess that’s a sign that I shouldn’t cheat and figure it out myself.

    1. Oh, and by the way it is out there on the interwebs… but they call it the “masters of logic” puzzle and it’s with red and blue dots instead of the crosses in my grandfather’s version. Mike nailed it below, however.

  3. The only thing I could deduce is the man knew because the other two men didn’t know (which he knew because of the 30 seconds)

    1. I should clarify there is actual logic involved, though the answer is the same.

      Since the guy sees that both other guys have black crosses he knows either he has black or white, but if he had white and because everyone tapped on their chair then the solution is trivial for either of the other guys and they should have solved it in less than 30 seconds. Since they did not then he must have black.

      1. I read your first reply before bed and had planned in the morning to come say “correct, but…” and give the explanation. But, you beat me to it. This is the right answer, and in almost the same words my grandfather explained it to me originally. Kudos.

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