**From New Scientist #2646, 8th March 2008**

I asked some friends to put the letters C, L, X, V or I in each of the boxes of the IV × IV square so that each row, each column (read from top down) and both diagonals (also read downwards) form 10 different valid Roman numerals less than CC, and then add the total of the 10 numbers to give a “score”. Twelve solutions were found, but Pauline noticed that one pair of solutions had scores differing by C, and Robert noticed another pair whose scores differed by C. The scores of Pauline’s pair were both divisible by V.

What were the scores of Robert’s pair? (Give the answer in Roman or Arabic form).

The posting of this puzzle completes my continuous run of *Enigma* puzzles from when I started doing them every week – with **Enigma 1482** – to the most recent puzzle published – **Enigma 1725**. I’ll keep posting new puzzles as they appear in *New Scientist*, and also carry on filling in the gaps in my list with old puzzles as long as I can find the text of them. Enjoy!

[enigma1484]

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In order to get only twelve squares you have to disallow the special case IIII as a permissible representation of 4. The following Python code uses the

int2roman()androman2intfrom myenigma.pymodule and runs in 488ms.Solution:The scores for Robert’s pair are 648 and 748.