a give rep to b x1
b give rep to c x2
b give rep to d x1
c give rep to e x1

a:b 1/1 = 1
b:c 2/3 = 0.6666
b:d 1/3 = 0.3333
c:e 1/1 = 1

a:b:c:e = 1 * 0.6666 * 1 = 0.6666
a:b:d = 1 * 0.3333 = 0.3333

mint and pay 1 rep

It would be better just to get the lowest value after each hop, less computation (and more accurate representation):

a give rep to b x1
b give rep to c x2
b give rep to d x1
c give rep to e x1

a:b 1/1 = 1
b:c 2/3 = 0.6666
b:d 1/3 = 0.3333
c:e 1/1 = 1

a:b:c:e = 0.66666
a:b:d = 0.333333

20 hops max is good.