First rearrange the problem to something a bit more useful:
1/12=1/c-1/b
So we know that c and b will be relatively close together, with c slightly less than b. The first, and most obvious solution is c=3, b=4, so we have 1/3-1/4=1/12.
It's also obvious that this is the smallest possible value, so we'll try some larger values. Of course, if c is any bigger than 12, it's impossible to find b (it would have to be infinitely big!) so we only have to try values of c between 3 and 12. Now it's just a simple search.
First we find c=4, b=6.
The next solution is c=6, b=12, since 1/6-1/12=1/12.
There are 4 same varieties. Label squares A to H left to precise, and a million to eight proper to backside. Then the trend is: A1 B1 C1 D1 E1 F1 A2 E2 F2 G2 E3 F3 G3 E4 G4 F5 different 3 same varieties obtained via consecutive ninety degree rotations.
Comments
First rearrange the problem to something a bit more useful:
1/12=1/c-1/b
So we know that c and b will be relatively close together, with c slightly less than b. The first, and most obvious solution is c=3, b=4, so we have 1/3-1/4=1/12.
It's also obvious that this is the smallest possible value, so we'll try some larger values. Of course, if c is any bigger than 12, it's impossible to find b (it would have to be infinitely big!) so we only have to try values of c between 3 and 12. Now it's just a simple search.
First we find c=4, b=6.
The next solution is c=6, b=12, since 1/6-1/12=1/12.
Next we have c=8, b=24.
Then c=9, b=36.
Finally c=10, b=60, and that's our last answer!
I think the answer is "no solutions" because anything you put for b would require a number greater than 1 above c.
for example:
1/12 + 1/2 = 7/12
1/12 + 1/6000 = 501/6000
I think it works like that for every number
edit: well 1/12 + 1/12 = 1/6... maybe I'm wrong... sorry
There are 4 same varieties. Label squares A to H left to precise, and a million to eight proper to backside. Then the trend is: A1 B1 C1 D1 E1 F1 A2 E2 F2 G2 E3 F3 G3 E4 G4 F5 different 3 same varieties obtained via consecutive ninety degree rotations.