**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?

[enigma1319]

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*Related*

This Python3 program uses the

int2roman()function from theenigma.pylibrary. It runs in 62ms.Solution:The common score is 246.The two designs are:

The numerals in braces may appear in either order.

We could simplify the search by noting that the only available 7 letter Roman numeral is 38, and so only consider even numbers.