Equivalent Resistance

Let the a battery be connected between A to B.Let us assume that current flows from A to B.
Consider the following 2 cases:

(i)Current I flows from A and spreads outwards(to infinty).
The net current flowing through the branch AB= \mathbf{I/6}}.

(ii)Current I comes in from infinity and leaves from B.
The net current flowing through the branch AB= \mathbf{I/6}}

Hence by the principle of superposition current flowing through AB = \mathbf{I/3}}

Equivalent resistance = R/3