Good one ..
1) each one has different colours
2) Exactly one of the statement can be correct

My arguments is like this
If X is Red is True then Y is not Red will also be true which violates second condition .
So X is RED not possible
Hence X cannot be true ( so X is White or Blue)

Now Y is not Red is True imply Y is White or Blue
Suppose Y is Blue then third statement will be True Not possible
Y is White then X will become Blue again third statement also become true.
Hence Y is not red is False So Y is RED...
Z can be White or Blue But since only one statement is True Z is Blue Hence X is White
Y= Red
Z= Blue