USAMO 2013 — Days 1 and 2 Question 3

Arrange $n(n+1)/2$ black-and-white tokens in an equilateral triangular array with $n$ tokens in the largest row, initially all white. An operation flips every token on a line parallel to a side. A configuration is admissible if finitely many operations produce it. For admissible $C$, let $f(C)$ be the minimum number of operations producing $C$. Determine $\max_C f(C)$ for every positive integer $n$.

Proposed by Warut Suksompong (as credited in the supplied compilation).