-2
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ Could you clarify if you want numbers between 1 to 8 or 1 to 9? And welcome to Puzzling!!! $\endgroup$ – Sid Nov 26 '16 at 7:22
  • $\begingroup$ 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? $\endgroup$ – Oray Nov 26 '16 at 21:28
1
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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

Clarification - I had initially posted an answer that had 0 in it, but I hadn't read the rules and so, I have changed my answer.

$\endgroup$
  • $\begingroup$ But 0 is not allowed (only numbers 1 to 9).... $\endgroup$ – PuzzleMaker Nov 26 '16 at 6:37
  • $\begingroup$ @PuzzleMaker 1-8 or 1-9? Sorry, I misread as 0-9.. $\endgroup$ – Sid Nov 26 '16 at 6:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.