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My dad really likes mechanical puzzles and has drawers full of them to show to people. My family has decided that it would be a great joke to find a new one that he hasn't seen, that is actually impossible to solve. Of course we wouldn't tell him that though. Does anyone know of any puzzles that fit that bill?

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The SE math stack has one here. It is known as the "Figure Eight Puzzle" and is a "disentanglement" puzzle.

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  • $\begingroup$ That sounds great! I wonder if anywhere actually still sells this, or if I'll need to make my own. $\endgroup$ – Raistlin Jan 6 at 20:39
  • $\begingroup$ Isn't "SE math stack" redundant? $\endgroup$ – Peregrine Rook Jan 7 at 23:52
  • $\begingroup$ @PeregrineRook it could quite possibly maybe be so. $\endgroup$ – Jonathan Allan Jan 8 at 0:40
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It might be too well known, but Sam Lloyd's 15 puzzle is famously known to be impossible:

Slide the numbers within the frame to get the numbers in order (ie swap the 14 and 15) \begin{array}{rrrr} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 15 & 14 & \end{array}

Another famous one, which you might be able to make easily with cardboard or wood if you're handy, is to place thirty-one 2x1 domino tiles onto a chess board with two diagonally opposite squares removed. Each domino covers two adjacent squares.

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  • $\begingroup$ Came here to mention the 15-puzzle one. It also generalizes to be unsolvable for any board configuration that's an odd number of swaps away from the solved state. $\endgroup$ – tilper Jan 7 at 19:23
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I've read a book which featured just this kind of a puzzle recently.

In Red Sister/Gray Sister (don't recall which volume it was) by Mark Lawrence, there is a test which involves getting to a place without being noticed, finding a puzzle box there and opening it (which had a bunch of puzzle locks on it - this part of the description is vague). Nobody has ever succeeded on the last step, because the box was not actually a box, but a solid block of wood with the locks serving as red herring.

I don't know whether any such puzzle are for sale though.

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