Fourteen identical resistors each of resistance r are connected as shown. Calculate equivalent resistance between A and B.

When a cell is connected between A and B, the current entered at A from the cell divides into two equal parts into the branches AC, AD. Hence the potential drops in them and the potentials at C, D will become equal. The resistor between C, D will become in effective and the resistors between AC and AD will become parallel. In the same way the resistors between EB and FB will become parallel. R_CG and R_GE are in series and their effective is parallel to the resistor between C, E. 
$\therefore {\mathrm{R}}_{\mathrm{CE}}=\frac{2\mathrm{r}\times \mathrm{r}}{2\mathrm{r}+\mathrm{r}}=\frac{2\mathrm{r}}{3}.$Similarly ${\mathrm{R}}_{\mathrm{DF}}=\frac{2\mathrm{r}}{3}$
Now the remaining equivalent circuit is given below
 

Now${\mathrm{R}}_{\mathrm{AC}}=\frac{\mathrm{r}}{2},{\mathrm{R}}_{\mathrm{CE}}=\frac{\mathrm{r}}{5},{\mathrm{R}}_{\mathrm{FB}}=\frac{\mathrm{r}}{2}$
$\therefore {\mathrm{R}}_{\mathrm{AB}}=\frac{\mathrm{r}}{2}+\frac{\mathrm{r}}{5}+\frac{\mathrm{r}}{2}=1.2\mathrm{r}$