= Solution
In a decelerating universe the comoving Hubble radius grows, so regions now in causal contact extrapolate to many disconnected early Hubble patches. Inflation shrinks the comoving Hubble radius and stretches one causal patch beyond the present horizon. Radiation scaling gives a present-horizon physical size at $10^{-35}$ s of roughly $ct_0(a/a_0)\sim ct_0(t/t_0)^{1/2}\sim1$ m. Comparing this with the inflationary Hubble length (about $ct\sim10^{-27}$ m at that epoch) requires $e^N\sim10^{27}$, or $N\simeq62$ (order 60).
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