Place one of the letters C, L, X, V or I into each of the 25 cells of a 5x5 grid so that each row and each column forms a 5-letter roman number under 300 (using the modern standard subtractive notation in which IV = 4, IX = 9, XL = 40, XLIX = 49, XC = 90, etc.). No roman number is used more than once, so there are ten different roman numbers. The rows are in descending order of value top-to-bottom and the columns are also in descending order left-to-right.
What is the sum of the values of the ten roman numbers?
C C L X X =270
C L X X X =180
X X X V I =36
X X V I I =27
X V I I I =18
= = = = =
2 1 7 2 2
3 7 6 7 3
0 5
270
180
36
27
18
230
175
76
27
+ 23
----
1062
There are 66 five-character roman numbers less than 300 all of which start with either C, L, or X.
Hence the first row and the first column cannot contain any Vs or Is.
There are only three of the 66 that contain no Vs or Is - CCLXX (270), CCXXX (230), and CLXXX (180)
From that we can tell that the top left cell must contain a C
and the last two cells of the first row and the first column must be Xs.
Analytically speaking that's as far as I got and I trial-and-errored the rest. I don't know if my solution is unique or not.
A solution
