I cultivate cells on semi-solid medium in a round plate. What is the number of cells to seed and what diameter of colonies should grow to achieve a 99% monoclonality? I have found an article https://www.genengnews.com/gen-articles/using-clonepix-fl-to-assess-monoclonality/3091/?page=2 . It says that Probability=(0.25 x π x (2d(c))2 x (n-1) / (0.25 x π x (2d(w))2) When colony number n=25, the diameter of the colony (d(c) ) = 0.75mm and the diameter of the well (d(w) ) = 35 mm.

But this formula looks amateurish: we can cut the same part at the bottom and the top of the equation.

Then I read the presentation https://www.topbiox.com/wp-content/uploads/2016/09/Impact-of-imaging-systems-on-probability-of-clonality-1.pdf . And on page 31 the same formula for different parameters of number colonies and diameter colonies on the plate gives different results during recalculating (look at pic).

Maybe there is another formula?

Below articles looks very difficult.

https://pdfs.semanticscholar.org/1917/018b4ece826503490a155f0062c8f34d58e1.pdf

https://stats.stackexchange.com/questions/17954/probability-of-circles-intersecting