Current observational limits on the density of magnetic monopoles tell us that their density parameter is currently ΩM,0<10−6. If monopoles formed at the GUT time, with one monopole per horizon of mass mM=mGUT, how many e-foldings of inflation would be required to drive the current density of monopoles below the bound ΩM,0<10−6? Assume that inflation took place immediately after the formation of monopoles.