---

Source. The bracketed note dated 19 August 1982 at the end of p. 54, of P. Erdős, Combinatorial problems in geometry, Math. Chronicle 12 (1983), 35--54, the transcript of an invited address at the 17th New Zealand Mathematics Colloquium (Dunedin, 17--19 May 1982), as named on the source card. The lecture numbers none of its statements; the pages are the journal's own.

Statement

Problem (p. 54). Let $h(n)$ be the largest integer such that any $n$ points in the plane with no three on a line and no four on a circle determine at least $h(n)$ distinct distances. Determine or estimate $h(n)$ as well as possible.

Read depth. Claims checked: the note was read clause by clause on the page image of the print. A second reader checked the statement, hypotheses, label and page against the print.

Proof pointer

The note proves nothing about $h(n)$.

Dependencies

question_p53, whose general-position condition the note keeps.

Bears on

• Problem 98: the note defines the problem's $h(n)$ and asks to determine or estimate it; the problem's question whether $h(n)/n\to\infty$ is one way to make that request precise. The note gives no bound.