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A bit of analysis gives us the solution straight away. So there’s not much for a program to do.

If we consider each pair of academics,

AandB, then if they combine their collection they have some (non-empty) set of missing issues,m(A, B), and every other academic must have these missing issues in his collection. This implies that all the sets,m(A, B), must be disjoint.So to minimise the number of issues of the magazine we make the sets,

m(A, B)as small as possible, i.e. each set contains exactly one issue, and as they are disjoint there is exactly one issue for each pairing of the academics.Hence the total number of issues is

C(12, 2).Solution:The number of issues ofMetacritical Quarterlyis 66.There is essentially only one way to achieve the solution. For each issue of the magazine there is exactly one pair of the academics that are both missing that issue and the remaining academics have it. So (modulo renaming) the distribution of magazines looks like this:

(The black squares indicate where an academic has the issue and the red squares indicate where they are missing an issue).

Each academic has 55 issues and is missing 11 issues.

So I don’t have to add this puzzle to the Unsolved Programatically list, here’s a Python program that demonstrates the distribution of the magazines and verifies that if any any three of the academics pool their collection they have a complete set of journals.