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March 28, 2017

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The letters A,B,and C represent three different digits. Determine the number ABC if ABC
+ ACB
----------
BCA

  • Math - ,

    What three different digits are represented by X,Y,Z in this addition problem?
    XZY + XYZ = YZX

    Just another perspective:

    1--First, from the last column, we could have either Y + Z = X or Y + Z = 10 + X
    2--From the second column, we could have either Y + Z = Z or Y + Z + 1 = 10 + Z
    3--But we can't have (Y + Z) equaling both X and Z, so Y and Z must add up to more than 10.
    3--Now we have Y + Z = 10 + X and Y + Z + 1 = 10 + Z or Y + Z = Z + 9.
    4--Equating (Y + Z)'s, we get 10 + X = Z + 9 or X = Z - 1
    5--Knowing that Y + Z exceeds 10, we can say 2X + 1 = Y
    6--Substituting, we get 2X + 1 + Z = 10 + X or X = 9 - Z
    7--Equating our expressions for X we get 9 - Z = Z - 1 or 2Z = 10 and Z = 5.

    I thing the rest should fall out fairly easy for you.

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