On a Reconstruction Problem of Harary and Manvel

We give a complete answer to a question raised by Harary and Manvel in 1972 (Bull. Soc. Math. Belg.24, 375–379) by proving that a finite set A of points in the plane R2 is uniquely determined up to translation and rotation by a multiple of 90° by 5 of its (∣A∣−1)-element subsets given up to translation and rotation by a multiple of 90°. This result is best possible.