It happens too rarely: stumbling across a method of clever simplicity.
Take the ecologist's way of estimating populations:
catch a sample and mark the specimens then release them.
After enough time for the sample to have mixed well with the local
population,
take another sample, mark them differently and note how many were marked
in the previous sample.
The population estimate can be generated from just this data - though
follow on samples would usually be taken.
The estimated population is given by the first count times second count
divided by the number
re-caught of those marked first time.
Justification: it is reasonable to suppose that the number in the second
sample includes the number previously marked
in a similar ratio to the number in the entire population compared with
the number in the first count.....