Kenneth Rosen Edition 7 Exercise 6.2 Question 38 (Page No. 406)

Question

Find the least number of cables required to connect eight computers to four printers to guarantee that for every choice of four of the eight computers, these four computers can directly access four different printers. Justify your answer.

Answer 1

Say the computers are C1, C2, C3, C4, C5, C6, C7, C8 and the printers are P1, P2, P3, P4

Connect C1 to all printers

Connect C2 to all printers

Connect C3 to all printers

Connect C4 to all printers

So no. of cables=4*4=16

Now connect C5-P1, C6-P2, C7-P3, C8-P4

So min 16+4=20 cables are required

If we pick any set of computers then all 4 different printers can be accessed

Say we pick the set C5, C6, C7, C8. We can access all different printers

Or we pick C1, C5, C6, C7. Still we can access all different printers

Max we can have is all computers are connected to all printers.In that case 8*4=32 cables would be required