Can 2001 numbers be all positive?
Source: Turkey TST 2001 - P1
April 5, 2013
functiongraph theorycombinatorics proposedcombinatorics
Problem Statement
Each one of children chooses a positive integer and writes down his number and names of some of other children to his notebook. Let be the sum of the numbers chosen by the children who appeared in the notebook of the child . Let be the sum of the numbers chosen by the children who wrote the name of the child into their notebooks. The number is assigned to the child . Determine whether all of the numbers assigned to the children could be positive.