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(Alright, how many ben gilo's.)
The Gemara in BM 30b says that each ben gilo visitor to a sick person eliminates 1/60 of their sickness by taking it upon himself. Presumably this means 1/60 of what's left after previous visitors took their portions, not 1/60 of the original. Thus, the disease can't fully be eradicated in this method. But it can get pretty close. How many visitors are needed to get to this point?
Depends how close you want to get.
(These are the days I wish Mi Yodeya supported MathJax.)
Each person leaves with 1/60 of the guy's sickness. Thus, for x visitors, the choleh is left with (59/60)^x of his disease.
Now, let's say we want to find out how many people need to come to leave him with 10^(-n) of his sickness, for some n (for example, a millionth, 10^(-6)). We can take the log of both sides and solve for x.
log((59/60)^x)=log(10^(-n))
xlog(59/60)=-n
x=137.000588091n
So, for whatever exponent you choose to plug in for n, multiply it by about 137 to figure out how many people need to come to get his sickness down to that point. In our above example of 10^(-6), that would be 6*137=822 ben gilo's.
EDIT: In Vayikra Rabbah (34:1), as the Matnos Kehunah understands it, R' Huna's talmidim originally understood this to mean sixty people should go around curing everybody. R' Huna replied that they remove one-sixtieth of the original if they love the sick person like themselves, but they will remove one-sixtieth of what remains otherwise. According to Maharzu, they remove one-sixtieth of what remains only if they love the person like themselves and they merely provide emotional support but don't remove any of the sickness otherwise. This version makes no mention of a Ben Gilo.
