A very interesting estimation problem I stumbled upon:
Suppose one is an Allied intelligence analyst during World War II, and one has some serial numbers of captured German tanks. Further, assume that the tanks are numbered sequentially from 1 to N. How does one estimate the total number of tanks?Read this guardian article for the interesting story about how this was a real problem in World War II and how the solution helped Allies win the war. Read the solution on wikipedia or this blog. The intuition is that the maximum of the 'captured' serial numbers as well as the number of captured serial numbers can be used.