
02310942
j
1996a.00451
Beck, I.
Bejlegaard, N.
Erd\"os P.
Fishburn, P.
Equal distance sums in the plane.
Normat 43, No. 4, 150161 (1995).
1995
Nationellt Centrum f\"or Matematikutbildning (NCM), G\"oteborgs Universitet, G\"oteborg
EN
G45
An equisum set in the plane is a finite set X$_n$ of distinct points $\lbrack{}$x$_1, x_2$, ..., $x_n\rbrack{}$ such that the sum of the distances from x$_i$ to all of the other points in X is the same for all i = 1, 2, ..., n. The authors show that an equisum set in which all the interpoint distances are different must have at least 5 elements. They also investigate the possible numbers of different interpoint distances in an equisum set with 5 elements.