Solution
= Solution
By planar duality on the triangular lattice, a finite open cluster containing the origin is surrounded by a closed circuit. If its diameter exceeds $n$, an outermost surrounding circuit reaches distance of order $n$ and crosses the positive coordinate ray at some $(m,0)$ with $m\geq c n$. Part (b3), with constants rescaled, therefore gives
$$
\mathbb P(0\text{ lies in a finite open cluster of diameter}>n)
\leq Ce^{-cn}.
$$