A quick Google says there's an estimate of 10^78 to 10^82 atoms in the universe. That number would be able to be stored in well under 300 bits.
Lots of problems suffer from 'combinatorial explosion' [1].
I recently learned about the Archimedes's cattle problem, the solution is of order 10^206544 [2]
[1] https://en.wikipedia.org/wiki/Combinatorial_explosion
[2] https://en.wikipedia.org/wiki/Archimedes%27s_cattle_problem
A quick Google says there's an estimate of 10^78 to 10^82 atoms in the universe. That number would be able to be stored in well under 300 bits.