Two Puzzles

Posted by jrosenhouse on August 23, 2012
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I am at a loss for good blog fodder today, so how about an amusing chess-themed puzzle I recently came across? It’s a simple question: What is it that the queen cannot do that a king, rook, bishop, knight or pawn can all do? Good luck!

Come to think of it, here’s another puzzle I’ve always liked. Nothing to do with chess this time. Imagine that you are in a pitch black room. No light at all. You are seated at a table. On the table is a standard deck of fifty-two cards, stacked neatly and squared away. Forty-two of the cards are face-down, while ten are face-up. Of course, since the room is completely dark you cannot see how the face-up cards are distributed within the pack. For all you know it could be the top ten cards that are face-up, with all the others face-down. Or maybe it’s the last ten cards that are face-up. Or the face-up cards might be distributed in some haphazard way. Your task is to divide the cards into two piles in such a way that the number of face-up cards in each pile is exactly the same.

Again, good luck!

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Comments

  1. #1 Eric
    August 23, 2012

    A queen is unable to capture a more powerful piece than itself.

  2. #2 Anton Mates
    August 23, 2012

    Haven’t played chess for about twenty years, but is a queen unable to reveal a discovered attack?

  3. #3 Iason Ouabache
    August 23, 2012

    A queen can’t pee standing up.

  4. #4 Anton Mates
    August 23, 2012

    And divide the cards into a pile of ten and a pile of forty-two, then flip the first pile upside down.

  5. #5 Michael Fisher
    https://secure.gravatar.com/michaeljfisher
    August 23, 2012

    When I realised that one pile needs to be turned over the answer fell out…

    Cut the cards into a a 10-pile & a 42-pile
    Turn the 10-pile the other way up
    The number of UP cards must now be the same in each pile

    Example [where U = Up & D = Down]:-
    If 42-pile = 7U + 35D
    Then 10-pile = 3U + 7D & turn it to get 3D + 7U
    Both piles now contain 7U

  6. #6 Michael Fisher
    https://secure.gravatar.com/michaeljfisher
    August 23, 2012

    The Queen cannot start on the other colour

  7. #7 JimR
    August 23, 2012

    This is for any reader of this blog who has never seen the riddle the Sphinx asked Oedipus:
    What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?
    Answer at: http://www.jimloy.com/puzz/sphinx0.htm

  8. #8 Wow
    August 23, 2012

    Answer: A shapeshifter.

  9. #9 Wow
    August 23, 2012

    Ask them why they want the cards so even when they turned the lights out?

    The “Wargames” resolution: don’t play is the only winning strategy.

  10. #10 Anton Mates
    August 23, 2012

    JimR: Ron Jeremy with a hangover.

  11. #11 James Sweet
    August 23, 2012

    Wow, I guess there are a lot of things the queen can’t do, because Eric, Anton Mates, and Michael Fisher all appear to have given valid answers! (I had to think about the discovered attack one for a moment, but yes that is true I think…)

  12. #12 Divalent
    August 23, 2012

    Many of the things I can think about the queen involve expressing a unique thing it can do as a negative it can’t NOT do. E.g. a queen cannot NOT attack any opponents piece that it happens to be legally moved immediately adjacent to. (A king can’t to this because it can never be legally moved immediately adjacent to the opponents king.)

    Cut the deck in half with a knife.

  13. #13 Jason Rosenhouse
    August 23, 2012

    This thread is starting to remind me of that old puzzle about finding the height of a building with a barometer. The intended answers, as others have pointed out are:

    (1) A queen cannot move to give discovered check.

    (2) Divide the cards into piles of 10 and 42, then flip over the pile with ten cards.

    But I like most of the other answers too!

  14. #14 MobiusKlein
    August 23, 2012

    use a standard Braille deck of cards. They are certainly standard for the blind.

  15. #15 qetzal
    August 23, 2012

    @Iason

    Sure she can. Although it may be messier than when the king does it!

  16. #16 NAL
    August 23, 2012

    For the card puzzle:

    Deal the first ten cards off the top and put them in one pile. Then turn the ten-card pile upside down. Voila.

  17. #17 MNb
    August 23, 2012

    Nitpicking alert.
    Actually Anton Mates mentioned a discovered attack, which not the same as a discovered check. So the question is: does the white queen attack the rook in a position like this?
    White: Qb2, Ba1
    Black: Kh8, Rg7, Ne8.

    White moves the queen away and discovers the attack.
    [/nitpicking]

    Still all honours go to AM. Despite playing chess for 30 years I would never have thought of it.

  18. #18 Zme
    August 24, 2012

    @qetzal:

    No hands! (c.f. Who can pee further…boy or girl)

  19. #19 Anton Mates
    August 24, 2012

    White moves the queen away and discovers the attack.

    Ah, fair enough. I didn’t realize that it’s still defined as a discovered attack even if the opponent’s piece was already under attack by your queen before you moved it. In that case, yeah, it would only be a discovered check that your queen can never reveal.

  20. #20 Richard Wein
    August 26, 2012

    My answers:

    1. What a queen can’t do is be something other than a queen.
    2. Cut the cards in half.

    I’m kicking myself for not thinking of the “right” answer to 2. I must admit I was too quick to give up and start thinking of silly answers.

  21. #21 crf
    August 29, 2012

    A queen cannot move to give discovered check.

  22. #22 Wow
    August 29, 2012

    Also can’t move like a knight.

    (if you’re not really interested in learning, you can “win” any argument!)

  23. #23 Lenoxus
    August 31, 2012

    Michael Fisher:

    The Queen cannot start on the other colour.

    I like this one, but it may not be true depending on the definition of “start”. When a pawn promotes to queen, that queen “starts” on a new square, which may be either color.

  24. #24 azoomer
    September 8, 2012

    darn, i didn’t figure out any of the puzzles.

    for puzzle #2, i thought i’d tear each card in half, and put half 1 in pile A and half 2 in pile B, and so on… =/

  25. #25 ME
    behind you...
    September 10, 2012

    the do not fear the laws of man or nature but they will definitely come fear this i hold…