Hi Chris
According to my trials with magnets and discussions with Dr Bonlie
(Magnetico) the absence of South pole is critical. A strong magnet does
not necessary have a much deeper field (the stronger is the flux, the
faster it want to joint with opposite pole). To ovoid south pole to
penetrate into the cylinder one has to cover it in a grid fashion. If
one has small magnets then there will be more of them. The distance
between each magnets is the maximum one you can allow without letting
the south pole "slip" in between. Strong neodymium are not necessarily
better in a cylinder or matress but can do wanders on a finger/toe
injury.
Mathias