ants and seeds
I have studied probability theory for some time, and I thought that I should not have too much difficulty to solve probability problems, but actually I still have quite a few probability problems unsolved.
This is a probability and combinatoric problem. It looks quite difficult at first thought but after I tried, it is actually not difficult at all. I recently began to use Lapack and I tried Lapack in this problem. The code runs quite fast, only 1.4 second, with some potential for further optimization.
After I solved this problem, I read some posts in discussion thread and luckytoilet's blog since I knew that he has two post about this problem (I resist the temptation to read it before I solved the problem). I am surprised to find that there is quite a few different approaches to solve it. I believe my method is quite straight forward and efficient. Maybe the combinatoric part scared the people.
Manually solve a 2x2 problem is helpful to solve the 5x5 problem.
Excellent problem! I like it.
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