Is it possible to create a 3 x 3 matrix, using only the numbers -1, 0, and 1 such that all six row and column sums are distinct?
***Adapted from OSSMB 84-7
There are only 7 possible sums: -3,-2,-1,0,1,2,3 since we need 6 of these sums, we must not use exactly one.
If a row sums to 3=1+1+1, no column can sum to -3 or -2.
Likewise -3 rules out +3 and +2.
If two different rows sum to 3 and -3, the only way to make the column sums different is to make the third row -1,0,1 but then this row and one column both sum to 0.
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Posted by Jer
on 2024-09-06 19:19:04 |
Slightly different solution
