# SOLUTION: AB x C = DE x F = GHI. the letters represent all numbers from 1-9. What is the number GHI? There are two solutions.

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 Question 617581: AB x C = DE x F = GHI. the letters represent all numbers from 1-9. What is the number GHI? There are two solutions.Answer by richard1234(5390)   (Show Source): You can put this solution on YOUR website!Best way is to brute force. However, there are several constraints: *5 can only go in A, D, G, or H (otherwise we'd be dealing with multiples of 5, contradiction). *1 can only go in G or H (if B = 1, AB*C would have last digit C, I = C, contradiction). If A = 1, the maximum value of AB*C is 18*9 = 162 --> G = 1, contradiction. If I = 1, B,C,E,F would all be odd. This means one of them must be 5, another contradiction. *I is even (If I were odd, A,C,E,F would all be odd. G or H is 1. *GHI is not a multiple of 11. With some Wolfram-Alpha quick-factoring, I obtained the following solution: 29*6 = 58*3 = 174 --> GHI = 174