Strange matrices from a dark auditorium...
Consider a matrix M, such that the sum of every row is the same as the sum of every column. That is, if you sum any row or column, it amounts to the same number. For example, with a sum of 18, M could be
9 2 7
4 6 8
5 10 3
Is it possible to construct a matrix M such that the sum of all its elements = 2^99 - 1?
Original problem courtesy six hours of trecherous pain during a training session a la the movie Office Space!
Note: Please include sisyphus' valid cribs in the comments section and the corrections concerning them...
9 2 7
4 6 8
5 10 3
Is it possible to construct a matrix M such that the sum of all its elements = 2^99 - 1?
Original problem courtesy six hours of trecherous pain during a training session a la the movie Office Space!
Note: Please include sisyphus' valid cribs in the comments section and the corrections concerning them...
posted by littlecow at 11/16/2005 02:44:00 PM
3 Comments:
Assuming conveniently (as I'm wont to do) that you are not looking for integer solutions.... If you take the matrix you give here and add (2^99-19)/3 to each element... would you consider the puzzle solved?
If you are looking for pure integer solutions, assuming M can be of any dimension, may I suggest a 1x1 matrix with 2^99-1 as the only element?
@sisyphus: your brave attempt at mitigating the limited veracity of my feeble question is appreciated. however, by imposing the abiding requirement of integer solutions on 3 X 3 matrices, i hereby condemn you, once again, to gyrate the rock up the hill...
Grenade rocks the house and moves up to 2nd place. Congrats!
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