# Adding up numbers in Portuguese is strange

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.

Could it be

   1246
+ 1246
------
2492 

Then

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

• Perfect! Easy one? – Chaotic Mar 20 at 4:50
• Not super easy, but there were a limited number of combinations to try. Good puzzle @Chaotic! – El-Guest Mar 20 at 11:28

From $$S+S=O$$ we know $$O$$ is even. From the $$O+O$$ part, we know $$O\le4$$ because $$2O$$ doesn't carry (otherwise $$O$$ would also have to be odd). Therefore $$I$$ is doubly even ($$I=2O$$), and because $$2I$$ doesn't carry, $$I=4$$ and $$O=2$$. $$D=S\pm5$$ and $$2D$$ doesn't carry, so $$S=6$$ and $$D=1$$. $$T=2I+1=9$$.

• You haven't given a value for $T$. – ZanyG Mar 20 at 5:54

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