"Rough estimate: 8 *109 people , Assuming a 10 cm2 signature/person to make the numbers easy. This comes from a 10cm long signature 1 cm in width.
Gives 8*1010 cm2 = 8*106 m2 in area. If we model the bat as a cylinder of length L, the surface area is SA = 2 pi r2 + 2 pi r *L, so if the bat has a length of 1 meter to fit in our hand, the second term is negligible, as r will be huge.
So A / 2pi = A/6 ~ 1 *106 m2 , square root to get the radius,
R = 1 * 103 m = 1 km
So if the bat is a meter long, it would have to be around a kilometer in radius to fit everyone’s signatures."
#20 Legibly. Or it would be completely black.