[DonRotolo]

OK, 15t and 32t, no problem.

If we assume a "long" chain, the wrap on each sprocket is about 50%, and the formula still works.

Let's assume a 'short' chain though, c-c around 4" maybe?

15t gets 7 links, not 7.5, because it doesn't wrap all the way around. YOU can calculate the exact number. If you don't know the geometry, try doing it graphically - draw it to scale on paper.

32t gets just a hair more than 16, call it 17.

7+17=24, a nice even number.

If we pick a distance as a multiple of 3.75, it would almost be perfect, except the chain is at a slight angle, so the chain needs to be a hair longer...or the c-c needs to be a bit shorter... than normal c-c. So if I pick 3.75", I'd go with 3.7 and accept a little looseness or 3.65 and struggle installing the chain.

Again, YOU can do the math to figure exactly how much longer 10 links will be at an angle of (need to figure that too...)

The whole point is, if you can do the math, it's just geometry and trigonmetry. If you can't, or need help, draw it out to scale on paper. (a 15t sprocket can be depicted with a (15*.375)/Pi diameter circle). Measure the angles or calculate them, both are perfectly acceptable methods. And, in your head, know the answer will be just a bit short of (N*.375), so if your method gives such a result, you can know you are spot on.