Question

in the following addition problem, each letter stands for a different digit.
Find the value of X, Y, and Z

XYZ
+ ZYX
_______
YYZY

Answer 1

xyz
zyx
*****
yyzy

Notice the leading digit y. It has to be 1. Think why. Now look at the middle digit of each number.It is 1. the last digit of the answer is 1.
What does that mean: Z+x=11
and then on the answer (y+y+carry 1)=3, so z=3

we have now as the puzzle
x13
31X
1131

and finally, x has to be 8.

Answer 2

zyzy