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Sum Rotation (Posted on 2004-05-11) Difficulty: 3 of 5
The numbers 1 through 9 are arranged in a 3 x 3 grid so that each number is in the grid exactly once. They are arranged such that the top row plus the middle row gives the bottom row. If the grid forms another such addition when it is rotated 90 degrees to the left, what is its composition?

(Note: The numbers don't flip, for example 6 doesn't turn into 9.)

No Solution Yet Submitted by Gamer    
Rating: 3.2500 (4 votes)

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General Observations | Comment 3 of 16 |
Alright... here goes. A slow day at work yields lots of fun on perplexus.

First start with a key:

ABC
DEF
XYZ

... for reference.

Now what I noticed is that B,C,E,and F are always in the added rows. I also noticed that X is always in the bottom row. Taking this observation, I figured one would have to make B+C+E+F = X and A+D = Y+Z for the system to work. Only problem is, it is impossible to make B+C+E+F = X because 1+2+3+4 = 10, X=9 best case senario. No big deal I thought, I will just make the A+D and Y+Z counterbalance each other. Not gonna work since the A+D comes down and the Y+Z goes up and no dice... Hopefully someone can use my observation to get to the answer.
  Posted by Scott on 2004-05-11 18:15:24
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