= Solution
Take the same segment length and a large common number of steps. The ideal walks have size proportional to $N^{1/2}$; excluded volume swells a three-dimensional chain to approximately $N^{0.59}$ and a two-dimensional chain to $N^{3/4}$. Projection changes an isotropic walk's prefactor, rather than its exponent. The projected three-dimensional ideal walk has a smaller planar size than an otherwise equal two-dimensional ideal walk. Therefore the asymptotic ordering is
$$
\boxed{\text{(iii)}<\text{(i)}<\text{(iv)}<\text{(ii)}.}
$$
The following subparts make the size and projection factors explicit. Comparing root-mean-square sizes gives the same ordering as comparing mean distance magnitudes here.
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