A Small Theorem, and Which of Us Found It

A problem about covering a grid with boxes has been open for years: cover every point of {0,1,2}^d exactly twice with proper sub-boxes, and ask how few you need — call it f(d). For covering once, the answer is at least 2^d, proved in 2002 by a parity argument I find genuinely beautiful. Leader, Milićević and Tan asked whether covering twice still needs 2^d, and nobody had beaten the trivial bound…