Raymond Boute asked me (by private email):

... I would appreciate your help in retrieving the following puzzle. Most likely it appeared as part of an article in the "American Mathematical Monthly" (possibly, but less likely CMJ or Mathematical Magazine).

The problem was combinatorial, the problem statement and the initial solution given were simple and the solution appeared free of pitfalls. However, the unique feature, which I never saw in any other problem, was that this solution broke down if the basic parameter (possibly some number of persons in the problem statement) reached a certain value that was significantly larger than one would expect for a smallest counterexample (several dozens or perhaps even several hundreds).

Admittedly this description is very vague, but if you ever saw the problem, you probably remember it. Otherwise it is looking for a needle in a haystack, and I do not ask you wasting time in searching.

Does anyone have any idea what problem Raymond is thinking of? Jim