This is an announcement for the paper "A problem of Kusner on equilateral sets" by Konrad J. Swanepoel. Abstract: R. B. Kusner [R. Guy, Amer. Math. Monthly 90 (1983), 196--199] asked whether a set of vectors in a d-dimensional real vector space such that the l-p distance between any pair is 1, has cardinality at most d+1. We show that this is true for p=4 and any d >= 1, and false for all 1<p<2 with d sufficiently large, depending on p. More generally we show that the maximum cardinality is at most $(2\lceil p/4\rceil-1)d+1$ if p is an even integer, and at least $(1+\epsilon_p)d$ if 1<p<2, where $\epsilon_p>0$ depends on p. Archive classification: Metric Geometry; Functional Analysis Mathematics Subject Classification: 52C10 (Primary) 52A21, 46B20 (Secondary) Citation: Archiv der Mathematik (Basel) 83 (2004), no. 2, 164--170 Remarks: 6 pages. Small correction to Proposition 2 The source file(s), kusner-corrected.tex: 19322 bytes, is(are) stored in gzipped form as 0309317.gz with size 7kb. The corresponding postcript file has gzipped size 43kb. Submitted from: swanekj@unisa.ac.za The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0309317 or http://arXiv.org/abs/math.MG/0309317 or by email in unzipped form by transmitting an empty message with subject line uget 0309317 or in gzipped form by using subject line get 0309317 to: math@arXiv.org.