Enigma 1319: Latin Christmas tree
From New Scientist #2477, 11th December 2004
My junior class has been studying Roman numerals. I asked them to replace each asterisk in the picture below with I, V or X so that each row formed a different valid Roman numeral, and either all were even or all were odd.
No letter was to appear in a row if it did not also occur in all the rows below it. When we totted up all the numbers appearing in each design, we found that Alice’s sum was the same as Barbara’s, although the individual numbers in their designs were not all the same.
What was this score?