The puzzle

I came across a very difficult puzzle. What number should be placed in that last slot? I only know 16 is not the correct answer, because 11 is before 10.

  • 1
    $\begingroup$ Is this one of those (rot13) uggcf://ra.jvxvcrqvn.bet/jvxv/15_chmmyr? If so this seems like it's one of those impossible-to-solve configurations. $\endgroup$ – Hugh Jul 3 at 6:03
  • $\begingroup$ No, it is not an impossible-to-solve configuration. $\endgroup$ – James Jul 3 at 6:08
  • $\begingroup$ (rot13) Gnxr 15 guna chg 0 gurer, guna lbh pna fbyir gur 15 chmmyr $\endgroup$ – Jamal Senjaya Jul 3 at 7:05
  • 4
    $\begingroup$ Welcome. Please can you clarify what the puzzle is. Have you put those numbers in that order, and we have find an extra number? Have you seen a picture of this puzzle and want to know how it works? To me this looks like a well-known type of puzzle where the task is to move the blocks around to get them in the correct order. There is meant to be a gap to allow room to slide blocks. In that case the final number doesn't exist. Please explain, thanks. $\endgroup$ – chasly - reinstate Monica Jul 3 at 11:52
  • $\begingroup$ @James - chasly above has done a good job trying to clear things up, but I'll extend on that. I believe that the "goal" of this puzzle is to slide the tiles around until they are in numerical order - 1 in the top left, reading left-to-right and top-to-bottom. It has been shown that some inital starting positions are "unsolvable" - link 1, link 2 $\endgroup$ – Hugh Jul 3 at 19:22

You misinterpreted the puzzle. You shouldn't place a number in the last slot; you should move them around so that the numbers are in order, i.e. from the shown position you need to swap the 11 and 10. It's a type of sliding puzzle, more than a century old, known as the 15-puzzle. Half of the starting positions of this puzzle are unsolvable, as is this particular one. It's rather easy to obtain Sam Loyd's position from this one.

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