# Solve XAB + YZCD = ZEXY

Replace each letter with a digit between 1 and 8 to make the equation

$XAB + YZCD = ZEXY$ true. Each letter represents a different digit.

Bonus question: How many solutions are there in total?

• Could you clarify if you want numbers between 1 to 8 or 1 to 9? And welcome to Puzzling!!! – Sid Nov 26 '16 at 7:22
• tkcs-collins.com/truman/alphamet/alpha_solve.shtml here is online solver... i am not sure what is different of this question ehich could be solved easily with an solver? – Oray Nov 26 '16 at 21:28

I've got another one (by which I mean another four):

$A=5,~B=2,~C=8,~D=4,$
$E=1,~X=3,~Y=6,~Z=7.$
\quad\qquad\begin{align}352\\+\quad6784\\\hline7136\end{align}
Solutions come in groups of four, because we can switch $A~$↔$~C$ and $B~$↔$~D$,
so we could also have $A=8,~C=5$ and/or $B=4,~D=2.$

I believe that Sid's answer(s) and mine are the only possible ones; i.e., there are eight solutions.

There could be more, but in base 10, I see 4 solutions:

Solution 1:

A=1 B=2 C=7 D=3 E=4 X=8 Y=5 Z=6 5673+812=6485

Solution 2:

A=1 B=3 C=7 D=2 E=4 X=8 Y=5 Z=6 5672+813=6485

Solution 3:

A=7 B=2 C=1 D=3 E=4 X=8 Y=5 Z=6 5612+873=6485

Solution 4:

A=7 B=3 C=1 D=2 E=4 X=8 Y=5 Z=6 5613+872=6485