The premise of the puzzle is quite simple. Here's how to set it up.

  1. Draw a 5x5 grid of squares.

  2. Write the number 1 in the middle.

  3. Make a "snake" of numbers up to 25 so that each number is orthogonal from the previous number AND the next number.

  4. Divide the grid into the pentominoes formed by the numbers 1-5, 6-10, 11-15, 16-20, and 21-25.

  5. If no two of the pentominoes are the same when rotated or reflected, you win. If two or more are, then you lose.


sorry for bad quality

This fails because 6-10 and 11-15 are the same, as are 16-20 and 21-25.

Is it possible to win this game? If your answer is no, prove it. If your answer is yes, give an example.

(I don't quite know how to tag this, feel free to edit some other tags in.)

  • $\begingroup$ I don't understand each number is orthogonal from the previous number AND the next number. Do you simply mean that n should be connected to n-1 and n+1, no matter in which direction? $\endgroup$ – Eric Duminil Nov 8 '18 at 8:13

If I understand the game correctly,

20,11,10, 9, 8
19,12, 1, 2, 7
18,13,14, 3, 6
17,16,15, 4, 5

  • 1
    $\begingroup$ I had a rotation of this. Well done! $\endgroup$ – Excited Raichu Nov 7 '18 at 18:20

I guess, I'm too late, but I propose

[A possible way]1

  • $\begingroup$ Nice! And looks "prettier" than mine! $\endgroup$ – Greg Nov 7 '18 at 18:27

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