[GFunk911]

they need to be odd or even, once u solve odd you +1 and solve for even. let's say they are even.

They all need to be a multiple of A apart, where A is some constant. A must be even for all numbers to be even or all odd. If they are not multiples of 2 apart, they can't all be odd or all be even, so they must be at least multiples of 2 apart.

Any 12-sum will have a sum of 12C + xA, where C is the smallest gear, A is the above constant and x is some number. In addition, each gear has the weight C + xA. The half-sum will be 6C + (x * .5A). The C is irrelevant. You can't make a sum of 6C + .5Ax with weights of C + Ax, unless A=0.