The positive integers are to be partitioned into several sets such that two times an integer and the integer itself do not belong to the same set, and every positive integer belongs to exactly one set. What is the minimum number of such sets required?
Sunday, August 19, 2012
Please email your solutions to firstname.lastname@example.org.
This puzzle is taken from:
- Savchev, Svetoslav; Andreescu, Titu. Mathematical Miniatures. Washington, D.C.: Mathematical Association of America, 2003. 36.