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Twice true (Posted on 2011-03-24) Difficulty: 3 of 5
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?

See The Solution Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

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Solution Solution! Comment 3 of 3 |
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
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