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Adjacent numbers (Posted on 2003-01-09) Difficulty: 3 of 5
A : 1
B : 2 C : 3 D : 4
E : 5 F : 6 G : 7
H : 8

Arrange the numbers in the grid above in such a way that no two adjecent cells (horizontally, vertically or diagonally) have consecutive number in them. For example 1 must not be next to 2. (The letters are shown so that you can easily refer to specific individual boxes.)

(From: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)

  Submitted by levik    
Rating: 3.1111 (9 votes)
Solution: (Hide)
There are a total of eight numbers that we need to distribute.

Cells "C" and "F" each have 6 adjacent cells. That means that whatever numbers we assign to these two cells, they will be surrounded by all the remaining numbers except for one. That means we cannot place a number in these cells if it has two neighboring numbers among the set. Thus, "C" and "F" must be populated by 1 and 8, since these numbers only have one neighbor.

Once we do this, the rest becomes fairly easy, yielding the final result:

            A : 7
   B : 3    C : 1    D : 4
   E : 5    F : 8    G : 6
            H : 2
Note that this can be "reflected" either horizontally, or vertically or both and the solution will still be valid, since such transformations do not alter adjacency.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle AnswerK Sengupta2023-10-30 23:03:18
SolutionEasy oneJim2004-08-06 14:30:49
SolutionSolutionLawrence2003-09-02 16:32:34
Solutiona thoughtJonathan Waltz2003-03-28 06:21:05
Adjacent numbersRavi Raja2003-01-11 07:12:40
re: Solution for adjacent numbersTomM2003-01-10 15:10:50
Solution for adjacent numbersRoxanne2003-01-10 09:45:53
Possible solutionAlison2003-01-10 08:18:47
SolutionNo SubjectTomM2003-01-10 07:35:17
Some Thoughtsstart..Cheradenine2003-01-10 03:05:41
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