Problem of the Week 814

An Odd Set of Positive Integers

This is the first problem posed by the new Macalester Puzzlemeister Tom Halverson (

Is there a set S of positive integers such that a number is in S if and only if it is a sum of two distinct members of S or a sum of two distinct positive integers not in S?

Source: This week's problem will soon appear in Which Way Did the Bicycle Go?...and other intriguing mathematical mysteries by Joseph Konhauser, Dan Velleman, and Stan Wagon; Dolciani Series, MAA (800-331-1622), September, 1996.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998