Difference between revisions of "2015 UMO Problems/Problem 5"
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==Problem == | ==Problem == | ||
| − | + | A <math>3 \times 3</math> grid is filled with integers (positive or negative) such that the product of the integers | |
| − | is equal to | + | in any row or column is equal to <math>20</math>. For example, one possible grid is: |
| + | <math>\begin{bmatrix} | ||
| + | 1 & -5& -4 \\ | ||
| + | 10 & -2 &-1 \\ | ||
| + | 2& 2& 5 | ||
| + | \end{bmatrix}</math> | ||
| + | In how many ways can this be done? | ||
== Solution == | == Solution == | ||
== See Also == | == See Also == | ||
| − | {{UMO box|year=2015|num-b= | + | {{UMO box|year=2015|num-b=4|num-a=6}} |
| − | [[Category:]] | + | [[Category:Intermediate Combinatorics Problems]] |
Latest revision as of 02:00, 6 November 2015
Problem
A 
grid is filled with integers (positive or negative) such that the product of the integers
in any row or column is equal to 
. For example, one possible grid is:
In how many ways can this be done?
Solution
See Also
| 2015 UMO (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All UMO Problems and Solutions | ||
