Adding up numbers in Portuguese is strange

Question

My friend from Portugal said that 2 + 2 is 8 in Portuguese. And he could prove it. I did not understand it at first. But then he showed me the following equation:

  D O I S
  D O I S
+ ________
  O I T O

Ah, now it is clear. Two is "dois" and eight is "oito" in Portuguese. And the equation above makes perfect sense. Could you solve the single one solution that explain this?

Rules: D, O, I, S and T are a number between 0 - 9. Each one is unique.

Answer 1

From $S+S\equiv O\pmod{10}$, we know $O$ is even. From $O+O$, we know $O\le4$ because $2O$ doesn't carry (otherwise $O$ would be odd because $D+D$ is even). Therefore $I$ is doubly even ($I\equiv 2O\pmod{10}$ and $O\equiv 2S\pmod{10}$), and because $2I$ doesn't carry, $I=4$ and $O=2$. $D=S\pm5$ (we have $D+D=S+S\equiv O \pmod{10}$), and $2D$ doesn't carry (otherwise there would be five letters in the answer), and so $S=6$ (because $O=2$, $S$ is either $1$ or $6$) and $D=1$. Finally, $T=2I+1=9$, so the sum is $1246+1246=2492$.

Answer 2

Could it be

   1246 

 + 1246 

 ------ 

   2492 

Then

D=1, O=2, I=4, S=6, T=9

Answer 3

Although this post is quite similar to JMP's answer, I still want to share it here:

4^th column: $O = 2 S$, therefore $O$ is even.
1^st column: $D < 5$, because $2 D < 10$.
2^nd column: $2 O$ must not carry, hence $O < 5$, so either $O = 2$ or $O = 4$.
4^th column: Therefore $D = O / 2$, so either $1$ or $2$.
1^st column: $S = D + 5$, so $2 S$ will carry and will make $T$ odd.
3^rd column: $I \neq 9$, because then $2 I + 1 = 19$, leading to duplicate $T = 9$ as well.
3^rd column: $I \neq 8$, because then $2 I + 1 = 17$, and the carry would force $I$ odd.
Hence $O \neq 4$, so the only possibility left is $O = 2$.
Thus, $D = 1$, $S = D + 5 = 6$, $I = 2 O = 4$ and $T = 2 I + 1 = 9 $.

Therefore, the result is:

$1246$
$1246$
--------
$2492$

Answer 4

Let's start as a basic Brute Force

Consider D as 1

 Since D and S gives a Unit Place as O

 So,S is D+5 ;S is 6

 So, Here O is 2

 Given I = O + O;     So,I=4

 Since T is I+I with a carry of 1 ;T is 9