If we cut  the wire of 100Ω, then resistance of each part will be $\frac{100}{\mathrm{n}}$.

When we connect these parts in parallel then equivalent resistance R = $\frac{100}{{\mathrm{n}}^2}$  (∵R = 1Ω)

So, n² = 100, n = ±10. We cut this wire into 10 parts to get 1 Ω resistance