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Solving the problem: A piece of land of a square shape with dimensions 10m x 10m is divided into 100 square parcels with dimensions 1m x 1m. Initially, 9 of the parcels are overgrown by weed. If a parcel is surrounded by at least 2 parcels with weed from its sides after some time that parcel will be overgrown by weed. Can the whole piece of land grow into weed after some time?

Alhazen's Billiard Problem: on a circular table there are two balls; at what point along the circumference must one be aimed at for it to strike the other after rebounding off the edge.

The 3n+1 conjecture, where if you take a natural number n and apply n/2 if its even or 3n+1 if its odd, repeat the sequence, you will eventually reach one.

These are just some examples of past papers. I would like an interesting topic that would be fun to research. This is for my IB Extended Essay. If you don't know what that is, it is a 4000 word research paper I need to write in order to get my IB diploma (that's a high school diploma).

I'm curious to see what topics you guys suggest! Thanks.