2
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The aim is to draw a single contiguous line from the upper left corner to the lower right corner. The line includes each number from 1 to 39 exactly once.

enter image description here

CSV:

 1,25,23,12,31, 3,20, 2,15,13,19,23
36,22,28,27,32, 4,19,21,20,11,29,12
34,13, 7,23,19, 8, 2,11,36, 8, 2, 3
 7,24,38,29,23,19,27,17,37,14,11, 7
 2,23,21,30, 6,20,38, 6,28, 9,33, 8
28,13, 9,11,36,18,16,15,11,18,34,14
 1,36,11, 2, 9,14,19,35,38,25,20, 7
20,21,33, 8,15,23,20,29,30, 5,32,18
10,34, 7,26,13,34,21,35, 9,13,16,17
15,37,23,22,24,18,24,37,29,24,26,10
31, 3,34, 8,27, 7,37,15,20,21,23,35
 7,29,17,14,26,23,24,18,36,20,19,39
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    $\begingroup$ Starting from top left, can I go directly to 22, or must I go through one of 25 or 36? $\endgroup$ – Weather Vane Apr 22 at 17:32
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    $\begingroup$ 25 or 36 only... $\endgroup$ – perayu Apr 22 at 17:34
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    $\begingroup$ @Deusovi I have added CSV format. $\endgroup$ – Daniel Mathias Apr 22 at 19:37
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    $\begingroup$ Are you sure [logical-deduction] is accurate? I've been at this for about half an hour and haven't found any logical path anywhere at all -- only case-bashing. $\endgroup$ – Deusovi Apr 22 at 22:34
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    $\begingroup$ I agree with @Deusovi, this requires a lot of guesswork. Highlighting the numbers that that occur less than four times will reveal likely portions of the path, even a few cells with certainty, but I don't see any logical solution for the complete path. $\endgroup$ – Daniel Mathias Apr 23 at 3:54
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This is my solution to the puzzle:

enter image description here

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  • $\begingroup$ Welcome! Can you perhaps provide a picture to show the path through the grid? $\endgroup$ – Beastly Gerbil Apr 23 at 19:56
  • $\begingroup$ I just realized the reason why my simulated annealing approach got so close but couldn't finish was because my cost function punished internal nodes in the path from being adjacent to any number of nodes not equal to 2. $\endgroup$ – Galen Apr 23 at 20:27
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My solution so far (incomplete). Eight more numbers to go (2,7,12,14,17,21,33,37):

Puzzle 1-39 partial solution

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