I thought the author of the original tweet that started this discussion might enjoy reading our explorations.

đź‘‡

I thought the author of the original tweet that started this discussion might enjoy reading our explorations.

đź‘‡

Thanks @apm - and an indirect "Hello!" to Christopher, if he continues to read this thread! :)

Christopher is correct pointing out at least one missing configuration, and I already found another one. The problem here really is that the asymmetrical interactions ("touching inside" and "contained") can lead to multiple variants being possible where I only considered one to exist.

This can happen if there (a) is more than one asymmetrical interaction, and (b) the remaining symmetrical interactions aren't all the same.

In many cases, it looks as if the variants aren't possible to draw - for example "A contains B, B contains C, C touches A on the inside" is a theoretical third variant of the alternative solution Christopher found, but one that's just impossible. Still, there are many potential configurations that still need to be checked.

(This, by the way, throws the whole "Tetrahedral numbers" tangent out of the window. ;))

Hello Factotum and apm, I have written a post with all the 48 possibilities I have found:

http://blog.radical-solutions.org/2019/04/intersections-of-three-circles.html

Please let me know if you find any that I missed!Hello @ChrisKlerkx - and welcome to Cake! :)

48 - I really missed a lot! I will have to study your images in more detail later, but looks great so far. Enumerating by number of intersection points is a nice idea. :)