0
$\begingroup$

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
  • 0
    Well even if it was a rule that it could be used, I don't think it is possible to have 0 as one of them anyways.2012-08-25

1 Answers 1

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.

  • 0
    @AaronWalker: We know $O=0$ from the ones digit of the second equation, which says $O+I=I$ (possibly, though not in this case, with a carry). This is one of the first things to look at when solving cryptarithms.2012-08-23