Question

find X , Y and Z if XXX + Y = YZZZ .

Answer 1

100x + 10x + x + y = 1000y + 111z
110x + ( x+y ) = 1000y + 111z

'.'X, Y, Z are digits,
x=9, y=1 is the only thing for which max(110x) is nearer to 1000y

Putting the values:-
1000 = 1000 + 111z
.'. z = 0;

Now, Let us assume y = 1, x = 8;
Then, 888 + 1 = 1ZZZ
which can't be equated if X,Y,Z represents unit digits....

.'. XXX + Y = YZZZ have only one soln. ,i.e., x=9, y=1, z=0