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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 '20 at 17:32
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    $\begingroup$ 25 or 36 only... $\endgroup$
    – perayu
    Apr 22 '20 at 17:34
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    $\begingroup$ @Deusovi I have added CSV format. $\endgroup$
    – Daniel Mathias
    Apr 22 '20 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 '20 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 '20 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 '20 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 '20 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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