Posted by Devin on Monday, February 14, 2011 at 11:19am.
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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