The following numbers have been picked at random from the set ${1,2,...,N}$. Numbers are: $212, 126, 382, 690, 1000, 739$. Estimate the value of $N$.

Question

The following numbers have been picked at random from the set ${1,2,...,N}$. Numbers are: $212, 126, 382, 690, 1000, 739$. Estimate the value of $N$.

I have no clue on how to start with this problem or any have any idea on what previous theorems i have to apply. Any help would be appreciated.

Answer 1

This seems to be what is known as The German tank problem.

During the Second World War, the Allies analysed the serial numbers of captured and destroyed German tanks and tried to estimate how many were constructed based on the known numbers. This seems to be exactly your problem.