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.)

in order to make 9, there are only two possibilities: 3-6-9 or 5-4-9 (when turned on its side, there is no way for three numbers to add up to 1 or 2). Also, this pattern must be placed in the first column, becuase when turned on its side, no number added to 9 can produce a number less than 9. we are now left with a grid which looks like this:

3 X X
6 X X
9 5 4
----
6 X X
3 X X
9 5 4
---
3 X X
6 X X
9 4 5
---
OR
---
6 X X
3 X X
9 4 5
----
with the 9 in the first spot, however, it is impossible for 9 to add to any number and yeild something less than 9.
Also, it is impossible to come up with a 3, 4, 5 or 6 when adding any number to 7 or 8.

when given the grid:
A B C
D E F
G H I

A+D=G, while C+B =A

maybe i'm missing something, but i don't think this one can be done

Posted by mike on 2004-05-11 18:59:08