A uniform wire of resistance 180 is cut into six equal segments....

Total resistance of the uniform wire $= 180 \Omega$

Since the wire is cut into six equal segments, the resistance of each segment is $\dfrac{180}{6} = 30 \Omega$

Three segments are connected in parallel to form a bundle. The resistance of this bundle is $\dfrac{30}{3} = 10 \Omega$

The remaining three segments are connected in series to form a chain. The resistance of this chain is $30 \times 3 = 90 \Omega$

The bundle and the chain are then connected in parallel. The equivalent resistance $R_{eq}$ of the entire arrangement is given by:

$R_{eq} = \dfrac{10 \times 90}{10 + 90} = \dfrac{900}{100} = 9 \Omega$

Answer: $9 \Omega$