# Puzzle regarding 100 random objects of different sizes, and choosing one at random one at a time to get largest

Basically, the riddle at hand was used to demonstrate a principle (of which I forgot), and it was asked thusly; I know there are other forms of it, but here goes:

You are fishing in a pond of 100 fish of unique sizes, you randomly catch one and need to decide to keep or throw it away. If you keep it, you acknowledge that this is the biggest fish in the pond and stop fishing, and if you throw it away, you acknowledge that this is the not the biggest fish in the pond and need to keep searching. When you catch a fish you remember the size. At what point do you say you have caught the second largest fish and the next largest fish should be the largest fish in the pond at the highest accuracy? I have calculated the optimal to be about the 34th fish using a brute force simulation, but I need the name of the algorithm/pattern/formula.

This is called the Secretary problem, and the optimal stopping point is at about $$\frac{n}e$$.