The Pentomino Snake











up vote
5
down vote

favorite
2












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.





Example:



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.)






tiling polyomino







share|improve this question
























  • 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?
    – Eric Duminil
    Nov 8 at 8:13















up vote
5
down vote

favorite
2












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.





Example:



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.)






tiling polyomino







share|improve this question
























  • 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?
    – Eric Duminil
    Nov 8 at 8:13













up vote
5
down vote

favorite
2









up vote
5
down vote

favorite
2






2





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.





Example:



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.)






tiling polyomino







share|improve this question















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.





Example:



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.)






tiling polyomino




tiling polyomino






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Nov 7 at 18:18









Weather Vane

98719




98719










asked Nov 7 at 18:00









Excited Raichu

4,233752




4,233752












  • 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?
    – Eric Duminil
    Nov 8 at 8:13


















  • 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?
    – Eric Duminil
    Nov 8 at 8:13
















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?
– Eric Duminil
Nov 8 at 8:13




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?
– Eric Duminil
Nov 8 at 8:13










2 Answers
2






active

oldest

votes

















up vote
8
down vote



accepted










If I understand the game correctly,




21,22,23,24,25

20,11,10, 9, 8

19,12, 1, 2, 7

18,13,14, 3, 6

17,16,15, 4, 5







share|improve this answer

















  • 1




    I had a rotation of this. Well done!
    – Excited Raichu
    Nov 7 at 18:20


















up vote
7
down vote













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




[A possible way]1







share|improve this answer























  • Nice! And looks "prettier" than mine!
    – Greg
    Nov 7 at 18:27











Your Answer





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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
8
down vote



accepted










If I understand the game correctly,




21,22,23,24,25

20,11,10, 9, 8

19,12, 1, 2, 7

18,13,14, 3, 6

17,16,15, 4, 5







share|improve this answer

















  • 1




    I had a rotation of this. Well done!
    – Excited Raichu
    Nov 7 at 18:20















up vote
8
down vote



accepted










If I understand the game correctly,




21,22,23,24,25

20,11,10, 9, 8

19,12, 1, 2, 7

18,13,14, 3, 6

17,16,15, 4, 5







share|improve this answer

















  • 1




    I had a rotation of this. Well done!
    – Excited Raichu
    Nov 7 at 18:20













up vote
8
down vote



accepted







up vote
8
down vote



accepted






If I understand the game correctly,




21,22,23,24,25

20,11,10, 9, 8

19,12, 1, 2, 7

18,13,14, 3, 6

17,16,15, 4, 5







share|improve this answer












If I understand the game correctly,




21,22,23,24,25

20,11,10, 9, 8

19,12, 1, 2, 7

18,13,14, 3, 6

17,16,15, 4, 5








share|improve this answer












share|improve this answer



share|improve this answer










answered Nov 7 at 18:09









Greg

1,802314




1,802314








  • 1




    I had a rotation of this. Well done!
    – Excited Raichu
    Nov 7 at 18:20














  • 1




    I had a rotation of this. Well done!
    – Excited Raichu
    Nov 7 at 18:20








1




1




I had a rotation of this. Well done!
– Excited Raichu
Nov 7 at 18:20




I had a rotation of this. Well done!
– Excited Raichu
Nov 7 at 18:20










up vote
7
down vote













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




[A possible way]1







share|improve this answer























  • Nice! And looks "prettier" than mine!
    – Greg
    Nov 7 at 18:27















up vote
7
down vote













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




[A possible way]1







share|improve this answer























  • Nice! And looks "prettier" than mine!
    – Greg
    Nov 7 at 18:27













up vote
7
down vote










up vote
7
down vote









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




[A possible way]1







share|improve this answer














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




[A possible way]1








share|improve this answer














share|improve this answer



share|improve this answer








edited Nov 7 at 18:25









gabbo1092

4,543635




4,543635










answered Nov 7 at 18:24









beemaad

35910




35910












  • Nice! And looks "prettier" than mine!
    – Greg
    Nov 7 at 18:27


















  • Nice! And looks "prettier" than mine!
    – Greg
    Nov 7 at 18:27
















Nice! And looks "prettier" than mine!
– Greg
Nov 7 at 18:27




Nice! And looks "prettier" than mine!
– Greg
Nov 7 at 18:27


















 

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