equals a multiple of 4. To explain this, note that we can split the

12 different single drafters into 4 groups of 3 (each group containing

3 drafters that are 120-degrees from each other), and the three

different ways of pairing these give the three parities. So one is

a+b-c-d, one is a+c-b-d, and one is a+d-b-c, where a,b,c,d represent

the 4 groups. Now, we actually take the absolute values of these

numbers, but since they are all even (guaranteed, since the total

a+b+c+d = 12, so each of these is the difference of two even or two odd

numbers), each is congruent (mod 4) to its absolute value. Anyway,

so the sum of the three parities is congruent (mod 4) to 3a-b-c-d,

or 4a (since a+b+c+d = 12 = 0 mod 4).

--Joseph DeVincentis