6

Part of 2008 IMAC Arhimede

Problems(1)

partition of {1,2,3, ..., 6024 } such that a=b+c, where a,b,c in S_1,S_2,S_3

Source: IMAC Arhimede 2008 p6

Consider the set of natural numbers

U = \{1,2,3, ..., 6024 \}

Prove that for any partition of the

U

in three subsets with

2008

elements each, we can choose a number in each subset so that one of the numbers is the sum of the other two numbers.

SubsetscombinatoricsSetspartition