I agree that it is unfair to students from non-top countries. Ironically, there are many very small countries at the top of IMO team resutls.

]]>Regarding the uniqueness of the generated y’s, I think it should be sufficient to invoke the identity:

arctan(1/y) = arctan(1/(y+1)) + arctan(1/(1+y(y+1))).

Since the given set S is finite, and since the algorithm described above generates only finitely many y’s, we could use this identity to “transform” the generated y’s to new values that are different from existing values in S and already generated values.

It is a pleasure reading your posts!

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