One More CryptArithmatic Problem

What three digits are represented by X, Y, and Z in this addition problem?

  XZY

+XYZ
______
  YZX

Here is the solution!

Solution Of One More CryptArithmatic Problem

What was the problem?

Here is the equation rewritten.

  XZY
+XYZ
______
  YZX
 

Let's start with the tens place. Z + Y = Z is there. That means either Y = 0 or 9 if 1 is carry from ones place.

Since Y is at hundred's place it can't be 0. Hence, Y = 9.

At hundred's column, now we have, X + X = 9. That's only possible if X = 4 and carry 1 forwarded from tens place. So X = 4.

Now, finally, at ones place, we have, 9 + Z = 4. Hence, Z must be 5 with carry 1 being forwarded to the next place.

To sum up, X = 4, Y = 9 and Z = 5.