I found two solutions

 C M 
MMMDC
 L X 
LXXXI
 I I

 M M 
MMMDC
 X X 
LXXXI
 V I

Gotta run, will check out the rest of the new stuff later.

Joseph DeVincentis


Hello again Ed,

Thanks for the hint, here is my solution:

Base 10 numbers = (81, 961, 1521, 3600)
Sum = 6163 is Prime
81 = 3^4
961 = 31^2
1521 = 39^2
3600 = 60^2

Roman numerals ( LXXXI, CMLXI, MDXXI, MMMDC )

Grid is filled out in the attached png.

That was a fun problem, thanks.

Later,
Andy Beatty

 
 I came across the "April Fool's Puzzle" on the mathpuzzle.com web site 
yesterday, and I was intrigued.  I believe I have a solution.

I suppose the big clue in the puzzle (and perhaps the reason why it's an April 
Fool's puzzle) was that the puzzle grid was found near Rome.  This led me to 
believe that the puzzle uses numbers represented in Roman numerals.

The two across numbers are (top to bottom):
 MMMDC (3600) and LXXXI (81).
The two down numbers are (left to right):
CMLXI (961) and MDXXI (1521).

(I'm not using a font that will lend itself well to putting them in the form of 
a diagram; sorry.)

All are perfect squares (of 60, 9, 31, and 39, respectively); and only 81 (the 
smallest, and on the bottom) is a perfect fourth.  Their sum is 6163, which (if 
my calculations are correct) is prime.

I hope that's the solution you were looking for!

-- Chris