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Round the square (Posted on 2004-07-30) Difficulty: 3 of 5
Can you place the numbers 1 to 8 on the outer squares of a 3x3 grid, so on every side the middle number is the sum of the corners next to it?

Can you manage to place the same numbers so the middle number of each side is the average of the corners next to it?

  Submitted by Federico Kereki    
Rating: 3.0000 (2 votes)
Solution: (Hide)
For the first problem:

1 7 6
4 - 8
3 5 2

7 and 8 cannot be on corners, while 1 and 2 must be in them, and the rest follows easily.

The second problem is impossible: 1 and 8 must go in corners, and no matter what other numbers go in the other corners, some middle row numbers would not be integers. (Next to the corner with the 1 we should have two odd corners so averages will be integer; for the same reason, next to the corner with the 8, we need two even corners; all together, this makes 6 corners!)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle ThoughtsK Sengupta2023-07-13 13:08:34
SolutionAnalytical evaluationLarry2017-10-31 11:25:57
Too EASY DRILL SARGENT!!Ron Dudley II2004-07-30 17:21:48
SolutionSolutionDJ2004-07-30 09:29:42
SolutionSolutionEric2004-07-30 09:11:51
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