Find pth percentile of a stream of numbers
I'm afraid that it is not possible to solve this problem with above conditions. Sooner or later, while reading next element from stream, you will run out of memory and will have to throw away one of buffered elements. But without having any constraints on further elements in stream, it is always possible to construct such sequence of further elements in stream, so that thrown out element is the searched one.

A practical commercial-grade solution exists, though it produces approximate result:


Allocate memory for as many numbers as you can afford
Use reservoir sampling atop of allocated memory to sample numbers from stream
When end of stream is reached, search for percentile among samples


To get exact solution, you need to either know number of elements in advance, or to have enough memory, or to have knowledge of stream properties (e.g. stream is monotonic). Keywords are "running median" and "n-th order statistics".