Below is a grid in which a latin square of numbers is to be overlain with a latin square of colors. That means each column and each row is to contain exactly one of each digit from 1 to 5, and exactly one of each color from among
light blue
pink
yellow
orange
light green
Besides that, each digit is paired with each color exactly one time in the whole grid. As you can see, no yellow is shown so far, but the rules are sufficient to place all colors (and numbers) correctly.
lord@rabbit 12945 % cw
square pair with good color distribution:
g3 y2 b1 o4 p5
p2 g1 y4 b5 o3
b4 o5 p3 g2 y1
o1 p4 g5 y3 b2
y5 b3 o2 p1 g4
I tried by hand and got as far as colors for row 4 and numbers for row 5 before opting for the less mentally taxing computer approach. I first thought to download all 56 (5x5) Latin Squares, but not finding a source, I generated what I needed.
While 130 pair overlays worked, only one pair had the uniform (pairwise) color distribution. If that pair is the only such pair _in the absence of constraints_ (which remains to be checked) it is truly a remarkable pair.
soln
