What are the digits that make this equation true in this cryptarithm?

Question

Can you find digits that make the equations true in the following alphametic puzzle (cryptarithm)?

$$RE + MI = FA$$ $$DO + SI = MI$$ $$LA + SI = SOL$$

• Zero may be a possible variable
• No one digit may be represented by more than one variable

Answer 1

From the second equation you have $O=0$. Also, since $SOL$ is the sum of two digit numbers, it follows that $S=1$.

Thus, so far we have

$$RE+MI=FA$$ $$D0+1I=MI$$ $$LA+1I=10L$$

From the last equation we get $L=8$ or $L=9$. Also, we know $D+1=M$ from the second.

Now, if each letter is a different digit, combining $E+I=A$ or $E+I=1A$ from the first equation with $A+I=L$ and $L \in \{ 8, 9 \}$, and studying the four possible cases should lead to the solution.