---

Claim. Every configuration of $17$ points in the plane, no three on a line, contains six points that are the vertices of a convex hexagon. This is the theorem of G. Szekeres and L. Peters, Computer solution to the 17-point Erdős--Szekeres problem, ANZIAM J. 48 (2006), no. 2, 151--164, cited as [SzPe06] on the problem page. The proof is a computer search over a combinatorial model of planar configurations, signature functions satisfying simple necessary conditions; the model covers more sign patterns than the realizable configurations, so the result proved is stronger than the geometric statement, and the authors report three independent implementations of the search. With the $16$-point set of the Erdős--Szekeres construction, which contains no convex hexagon, this gives, in the notation of Problem 107,

$$f(6)=17=2^{4}+1.$$

Covers. The instance $n=6$ of the conjectured equality $f(n)=2^{n-2}+1$. Not covered: every $n\ge7$, for which only the lower bound is known.

Depends on. The Erdős--Szekeres construction for the lower bound $f(6)\ge17$; the upper bound $f(6)\le17$ is the paper's own.

Acceptance. Refereed: the paper appeared in The ANZIAM Journal, a journal. The paper is not among the site's references, and the site labels the problem FALSIFIABLE, which settles nothing, so no reviewed evidence is listed. The computer search has not been rerun in this corpus.

Dating. The publisher's record dates the issue October 2006 and gives no day, so the day is a placeholder; the publisher's online date, 17 February 2009, is the later digitization of the volume.