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Claim. Every configuration of $2^n$ points in the plane, $n\ge3$, contains an angle strictly greater than $\pi(1-1/n)$ (Theorem 1). Combined with Szekeres's 1941 configurations, which show $\alpha_{2^n}\le\pi(1-1/n)$, this gives $\alpha_{2^n}=\pi(1-1/n)$, and the strict inequality shows that every $2^n$-point configuration has an angle strictly larger than $\alpha_{2^n}$. Theorem 2 gives $\alpha_{2^n-k}\ge\pi(1-1/n)-k\pi/(2(2^n-k))$ for $0<k<2^{n-1}$. A note added in proof sharpens the case $k=1$ to Theorem 3: every configuration of $2^n-1$ points, $n\ge3$, contains an angle not less than $\pi(1-1/n)$, so $\alpha_{2^n-1}=\pi(1-1/n)$ as well, the authors leaving undecided whether the inequality is strict there. The print states Theorem 3 for $n\ge2$, which is an error: at $n=2$ it would say that every triangle has an angle of at least $\pi/2$, which the equilateral triangle refutes, and the printed proof starts from a point of the configuration inside its convex hull, which exists only when $2^n-1$ exceeds the hull's at most $2n-1$ vertices, that is, for $n\ge3$. The paper also records $\alpha_3=\pi/3$, $\alpha_4=\pi/2$, $\alpha_5=3\pi/5$ and $\alpha_6=\alpha_7=\alpha_8=2\pi/3$, and the site's page also records $\alpha_{2^n}=\alpha_{2^n-1}=\pi(1-1/n)$.

Covers. The values of $\alpha_N$ at $N=2^n$ and $N=2^n-1$ for $n\ge3$ and for $N\le8$. The authors suggested that $\alpha_N=\pi(1-1/n)$ might hold for every $N$ with $2^{n-1}<N<2^n$ and $n\ge4$; Sendov refuted that in 1992 and determined every value from $N=4$ on in 1993, recorded on Sendov's claim page.

Source. The source card lists Theorems 1, 2 and 3 (the last from the note added in proof) and the small values; the same paper gives the $2^{n-2}$-point construction for the convex polygon problem, Problem 107.

Acceptance. The paper is refereed: P. Erdős and G. Szekeres, On some extremum problems in elementary geometry, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 3–4 (1960/61), 53–62. The curator of erdosproblems.com, Thomas Bloom, records the result on the problem page with this paper as its source; the site's label SOLVED credits Sendov's determination of every value, so the curator's mention is context for this partial claim and not acceptance evidence. The page is dated to the publication year, the record giving no day.