Here is a great puzzle from Ed Pegg Jr.

Place two coins in the center cell of the following grid. Now you can choose a coin X and move the second coin Y one cell in the direction of the arrow under coin X. Coins cannot leave the grid. Can you find a sequence of moves that bring both coins to their starting location in the center of the grid? Good luck!

Grid as an image

  • $\begingroup$ What exactly is the question? It seems there are both reachable states from which you can go back and reachable states from which you cannot go back (and non reachable states from which you could come back for that matter). $\endgroup$ Jan 8, 2021 at 2:29
  • $\begingroup$ The question is how do you bring both coins to the starting position? $\endgroup$ Jan 8, 2021 at 3:52
  • $\begingroup$ What I mean is: it depends. On the initial sequence of moves. Do you want a solution for any such sequence or am I allowed to choose it? $\endgroup$ Jan 8, 2021 at 4:16
  • $\begingroup$ I see where the confusion was. You need to find a sequence of moves that brings both coins to the starting position. I will rephrase the text in the puzzle. $\endgroup$ Jan 8, 2021 at 4:22
  • $\begingroup$ Just to be clear you can move X where you like - it's movement isn't governed by the tile Y is on? $\endgroup$ Jan 8, 2021 at 11:12

1 Answer 1


One of many:

--30 characters--

30 characters here I come

  • 1
    $\begingroup$ Nice work. Can you find a shorter solution? $\endgroup$ Jan 8, 2021 at 5:43
  • $\begingroup$ @DmitryKamenetsky with more than zero moves I assume? $\endgroup$ Jan 8, 2021 at 5:47
  • $\begingroup$ yes more than zero $\endgroup$ Jan 8, 2021 at 10:06
  • 2
    $\begingroup$ @DmitryKamenetsky I just checked with computer and it seems to be the shortest and uniquely so. $\endgroup$ Jan 8, 2021 at 10:37

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