In the figure, the value of resistors to be connected between C and D so that the resistance of the entire circuit between A and B does not change with the number of elementary sets used, is

Cut the series from XY and let the resistance towards right of XY be R₀ whose value should be such that when connected across AB does not change the entire resistance. The combination is reduced to as shown below.

The resistance across EF, = $R_{EF}=\left(R_0+2R\right)$

Thus ${\mathrm{R}}_{\mathrm{AB}}=\frac{\left({\mathrm{R}}_0+2\mathrm{R}\right)\mathrm{R}}{{\mathrm{R}}_0+2\mathrm{R}+\mathrm{R}}=\frac{{\mathrm{R}}_0\mathrm{R}+2{\mathrm{R}}^2}{{\mathrm{R}}_0+3\mathrm{R}}={\mathrm{R}}_0$

$\Rightarrow R_0^2+2R{R}_0-2R^2+0\Rightarrow R_0=R\left(\sqrt{3}-1\right)$