Question

how would you arrange three resistors each of 9 ohm in such a way to get equivalent resistance of 13.5 ohm

Answer 1

The only possibility to get 13.5 ohm is to connect the two resistances in parallel. 

In fact, 1/9+1/9 provides an equivalent resistance of 4.5 ohm. 

1/R=1/9+1/9=2/9 

R=9/2=4.5 

R (eq)=R+9= 13.5 

The last resistor should be connected to the network in series to get the desired result