A three stage switching structure supports 100 inlets and 400 outlets. Find the number of cross points, and the number of primary and secondary switches used in the design.

We identify that

m = M/ M+N and n = N/M+N

m = 100

1. When m=5, n=20, there are:

Primary switches are 20 of size 5 x 5

Secondary switches are 5 of size 20 x 20

Tertiary switches are 20 of size 5 x 20

2. When m = 4, n =16, there are:

primary switches are 25  of size 4 x 4

Secondary switches are 4 of size 25 x 25

Tertiary switches are 25 of size 4 x 16