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Place the numbers 1 to 25 on the cells of this board so that any two consecutive numbers occupy cells that are horizontally, vertically or diagonally adjacent. Prime numbers should occupy shaded cells.

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    $\begingroup$ I don't get it. A bishop's walk could only visit half the cells. Shouldn't it be a King's walk? $\endgroup$ Commented Sep 21, 2021 at 7:03
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    $\begingroup$ There are 8568 solutions (counting rotations and flips). These could be grouped into 192 permutations for the prime cells. The number 23 occurs in the middle ~72% of the time. $\endgroup$ Commented Sep 21, 2021 at 12:53
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    $\begingroup$ @EricDuminil Right! Fixed! $\endgroup$ Commented Sep 21, 2021 at 13:15

2 Answers 2

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Like so?

enter image description here

The beginning seems almost forced (apart from symmetries), and the rest just fell in place on the first attempt.

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  • $\begingroup$ Almost but not quite (forced, that is): 25 3 4 5 6 // 2 24 22 21 7 // 14 1 23 8 20 // 13 15 16 9 19 // 12 11 10 17 18 $\endgroup$
    – loopy walt
    Commented Sep 20, 2021 at 21:19
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As there are quite a few possible solutions and seeing that it is "A Bishop's Walk" here is one that tries to use as many bishopy (aka diagonal) moves as possible:

      1     3    25    23  - 22
      |  /  |     |  /     /
      2     4    24    21    19
               \           X  |
      8     6  -  5    18    20
      |  X                 \
      7     9    12    15    17
         /     /     X     \  |
     10  - 11    14  - 13    16
 

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