Proved, in the site's label, which credits Croot. Croot's Main Theorem (Acta Arith. 99 (2001), no. 2, 99--114; refereed) gives, for every $N>1$, integers $N<n_1<\cdots<n_k\le(e+o(1))N$ with $1=\sum1/n_i$, whose width is below $(e-1+o(1))k$ since $k>N$; the paper states the result "for infinitely many $k$". For every large $k$ the site's question is answered by Martin's Theorem 2 (Acta Arith. 95 (2000), no. 3, 231--260; refereed), the source of Problem 285: a $k$-term representation of $1$ with all denominators at most $(e/(e-1)+o(1))k$ lies in an interval of width below $(e-1)k$, because $e/(e-1)<e-1$. The standing in the frontmatter derives from the claim pages: the accepted full claim Martin 1998 and the accepted partial claim Croot 1999, which covers the infinitely many $k$ of Croot's construction with the sharper width.