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How many different arrays whose entries are all 1's and -1's have the property that the sum of the entries in each row is 0 and the sum of the entries in each column is 0?
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
- Reduce fractions to
lowest terms and enter in the form 7/9.
- Numbers involving pi should be written as 7pi or 7pi/3
- Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
- Exponents should be entered in the form 10^10.
- If the problem is multiple choice, enter the appropriate
- Enter points with parentheses, like so: (4,5)
- Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
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