LIX+LVI=CXV ; X*X=C
The above equations are true both as Roman expressions and as alphametics, where each letter denotes Arabic numeral. What is the unique solution?

X*X is a 1-digit number. Therefore, X is either 0, 1, 2, or 3. If X is 0 or 1, then X=C, but they are different letters. Therefore, X is either 2 or 3. Suppose X=2. Then, C=4. Then, L has to be 2, but X=2. Therefore, X=3, so C=9. L has to be 4. We now have 4I3+4VI=93V. Therefore, I+V=13 and 3+I=V. The solution is I=5 and V=8. The equation is 453+485=938.

Posted by Math Man on 2011-03-30 16:52:31