Enigma 1260: Latin fives
27 January 2015
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From New Scientist #2416, 11th October 2003 [link]
Your task today is to put one letter C, L, X, V or I into each of the 25 squares in the grid so that each row and each column (read downwards) forms a different valid Roman numeral. The sum of the numbers in the rows is to equal the sum of the numbers in the columns. Use the smallest number of Cs you can. As a hint, one of your diagonals will be a valid Roman numeral and the other will contain only one letter.
(a) the sum of the numbers in the rows (or columns); and
(b) the Arabic value of the valid diagonal?