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So let's say you find a small amount of numbered collectibles (e.g. 3 collectibles numbered 5, 14 and 103). Is there a way to estimate the total number of collectibles in existence?

Harry Thompson
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  • https://math.stackexchange.com/questions/704828/determining-total-number-of-tickets-sold and https://math.stackexchange.com/questions/762959/estimating-parameter-of-random-sample and https://math.stackexchange.com/questions/6648/license-plate-statistics and https://math.stackexchange.com/questions/455931/german-tank-problem-simple-derivation and https://math.stackexchange.com/questions/65398/why-does-this-expected-value-simplify-as-shown and https://math.stackexchange.com/questions/3002437/sum-of-reciprocal-numbers-of-combinations and surely many others. – Gerry Myerson Oct 13 '19 at 12:39

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This is the "German Tank Problem", addressed here and there among other places; see Ruggles, R.; Brodie, H. (1947). "An Empirical Approach to Economic Intelligence in World War II". Journal of the American Statistical Association 42 (237): 72 for the real scoop. In war time serial numbers on captured enemy equipment gives a clue about how many units might exist.

You can find other MSE postings by searching for "German Tank Problem".

The recipe is explained in the last two citations above.

Of historical or antiquarian interest, perhaps better suited to the history of science and mathematics SE: This problem is also known as the "Taxi" problem, and before that the "Trolley Car Problem", and some notables who were interested in it were Alan Turing, M.H.A. Newman, R.A. Fisher. It seems to have been first formulated as a math problem by Erwin Schroedinger.

kimchi lover
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