Facebook had conducted it's test on InterviewStreet in IITB. Total duration of test was 2 hours. The problem boiled down to following:
Given an undirected graph, source node s and destination node d; find number of distinct nodes visited on all paths from s to d such that each node is visited exactly once while enumerating all the paths.
The question above is fairly tricky to implement in an efficient manner. Surprisingly, the exact same coding question was also asked at other IITs as well as every other college in India where Facebook had gone for recruitment.