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If you really have to do this with only elementary tools, you can set up the equation⎛⎝147258369⎞⎠⎛⎝adgbehcfi⎞⎠=⎛⎝100010001⎞⎠This gives you 9 equations, but they can be divided nicely into groups of three by considering each column separately. For instance, we geta+2d+3g=1
0 0 0
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