Lollipop modelled on Desmos + a suggestion for a variant

[N A]

I noticed some folks here were playing with lollipops per Neil's posed problem.
I'm thinking of making a tool in Desmos that lets you play with these lollipops in an intuitive manner, unless someone else already has such a tool?

The idea is to let you drag around the centers to move the lollipops and add a second point right where the ray extends off where you can change where along the arc it starts. That second point (or maybe a third point opposite it) would let you change the size of the "lollipop".

But the real challenge to make this fully useful is to have Desmos count how many regions are encircled!

Also, I think a variant could be defined for multiple rays coming off of the circle, so instead of calling them lollipops, you'd call them wheel spokes.

It's really a good bit of fun!

[David desJardins]

On Fri, Jan 2, 2026 at 6:31 PM N A <narno...@gmail.com> wrote:

But the real challenge to make this fully useful is to have Desmos count how many regions are encircled!

As Neil explained, you don't have to count the regions, you just have to count the intersections. Surely that's not very hard. 

[David Radcliffe]

I made a simple web app to explore Neil Sloane's lollipop problem. Please excuse the vibe coding.

David

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[N A]

Intersections... I think Desmos can't do that either without some real effort that's better used on the actual problem.

But I did also manage to reach 44 with the web app + manually counting the regions in Desmos.