9
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Each letter shown represent distinct digit...can vary from zero to nine.

$COCA$, $COLA$, $SODA$ are three concatenated numbers.

Figure these out from the following relation:

$COCA + COLA = SODA$

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  • 1
    $\begingroup$ deleted image. feel free to rollback if needed :) $\endgroup$ – Omega Krypton Jun 17 at 8:40
  • $\begingroup$ Am I the only one who thought "Too early in the morning" was a hint? $\endgroup$ – Mr Lister Jun 18 at 12:10
  • $\begingroup$ I don’t know..when I got up little early yesterday, title popped in my head $\endgroup$ – Uvc Jun 18 at 12:13
13
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Based on Omega Krypton's answer,

$2C+1=S,C+L=D+10$, $A=0,O=9$. (Note that $O=9$ so $C+L$ carries.)
We also need that these digits $C,L,D,S$ are distinct between $1\sim 8$. ($0$ and $9$ are taken.)
If $C=1$ or $C=2$ then, since $D\ge 1$ we have $L\ge 9$ which is incorrect.
So $C=3$ and $S=7$. We have $L=8$ and $D=1$.
That is $3930+3980=7910$.

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  • 2
    $\begingroup$ hi, nice try! +1 $\endgroup$ – Omega Krypton Jun 17 at 8:55
  • $\begingroup$ Got it!!....deceptively unique $\endgroup$ – Uvc Jun 17 at 8:56
  • $\begingroup$ Yeah deceptively. :) $\endgroup$ – r_64 Jun 17 at 8:57
17
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We have the following

 COCA
+COLA
-----
 SODA

First, from the ones column, we have $A+A \implies A$ which is only possible if $A=0$.

Next, notice something similar in the

hundreds place; $O+O \implies O$. Since $0$ is already taken and the only possibility without a carry over, we must have a carry over from the 10s, and $O=9$ is the only possibility. We will also have a carry over into the thousands.

Since we have a 4 digit number as the result, we know that

$0 \lt C \le 4$.

But:

-But $C=4 \implies S=9$ which is already taken by $O$.
-And $C=1 \implies L=9$ to achieve a carryover, which is taken by $O$.
-And $C=2 \implies L\in\{8,9\}$. But $L=9$ is taken, and $L=8 \implies D=0$ is also taken.

Thus,

$C=3$.

Also, we know

$S=7$ because the hundreds will carry over, and we also know that in order to carry over the 10s, we need $L\ge 7$. But $L=7$ and $L=9$ are taken leaving only $L=8$, and thus, $D=1$.

Thus, the solution is;

COCA+COLA=SODA, 3930+3980=7910

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  • 2
    $\begingroup$ Easiest deductions for me =) $\endgroup$ – Montolide Jun 17 at 18:41
8
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Since we know that

$A+A \equiv A \pmod {10}$

Therefore $A$

$=0$

Hundreds value must carry since $O \neq 0$

Therefore

$O+O+1 \equiv O \pmod {10}$

Therefore $O$

$=9$

We now get

$2C+1=S$
$C+L=D$

And since $S<9$

$0<C<4$

Then there are many possibilities... any relations I missed out?

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  • $\begingroup$ On the right track..I think it is unique $\endgroup$ – Uvc Jun 17 at 8:51
  • $\begingroup$ Keep going..eventually you will get there $\endgroup$ – Uvc Jun 17 at 8:55

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