Home ยป Back to Unsolved Puzzles

box o' numbers

Puzzle Question: 

arrange the numbers 1 to 8 in the grid below such that adjacent numbers are
not in adjacent boxes (horizontally, vertically, or diagonally).
 

       ___

      | 1 |

  =============

  | 6 | 4 | 3 |

  =============

  | 2 | 7 | 5 |

  =============

      | 8 |

      =====
the arrangement above, for example, is wrong because 3 & 4, 4 & 5, 6 & 7, and
7 & 8 are adjacent.

Level of Toughness: 
Intermediate

The key (as I see it) is

Submitted by Anonymous on Thu, 2008-03-20 12:25.

The key (as I see it) is putting the 1 & 8 in the centre spots - which is required, because those spots both border all but one of the other spots, and 1 & 8 are the only numbers that are only adjacent to one number.
From there, the 2 & 7 are forced, then you have your choice of the next number, which then forces the rest. Really, though there are only two valid solutions, and they are mirror images of each other.

 
 

actually, there are 4 valid

Submitted by Anonymous on Mon, 2008-03-24 20:07.

actually, there are 4 valid answers as they are all mirror images of each other, but they can be reflected on both the X and Y axis



       ___       |       ___     

      | 7 |      |      | 7 |      

  =============  |  =============  

  | 4 | 1 | 3 |  |  | 3 | 1 | 4 | 

  =============  |  ============= 

  | 6 | 8 | 5 |  |  | 5 | 8 | 6 | 

  =============  |  =============  

      | 2 |      |      | 2 |      

      =====      |      =====      

-----------------|-----------------

       ___       |       ___

      | 2 |      |      | 2 |

  =============  |  =============

  | 6 | 8 | 5 |  |  | 5 | 8 | 6 |

  =============  |  =============

  | 4 | 1 | 3 |  |  | 3 | 1 | 4 |

  =============  |  =============

      | 7 |      |      | 7 |

      =====      |      =====