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How many solutions are there to satisfy the equation: ABC+BCD=CBA

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How many solutions are there to satisfy the equation: ABC+BCD=CBA where each letter represents one digit?

posted Feb 8 by anonymous

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1 Answer

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C + D = A + 10(carry)
1 + B + C = B + 10(carry)
1 + A + B = C
Therefore C = 9 and A + B = 8. So the possible solutions are
1. 089 + 891 = 980
2. 179 + 792 = 971
3. 269 + 693 = 962
4. 359 + 594 = 953
5. 539 + 396 = 935
6. 629 + 297 = 926
7. 719 + 198 = 917
ie. There 7 solutions.

answer Feb 17 by Tejas Naik
There are more solutions, please try harder
1. A, B, C, D can't be same
2. A, B, C can't be zero



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