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*Find the maximum number of elements that can be chosen from the set {1,2,3,...,2005}*

* such that the sum of any two chosen elements is not divisible by 3.*

Guest Feb 8, 2019

#1**+1 **

Here's my attempt....whether it's correct....I don't know....

Just a little trial and error

{ 1,4, 7, 10, 13,..... }

2004 is divisible by 3

So....2005 would be the next integer that is one more than a multiple by 3....which is also a characteristic of the integers in the first set

So....we can find the number of elements by

2005 = 1 + 3(n - 1)

2005 = 1 + 3n - 3

2005 = 3n - 2

2007 = 3n

n = 669 elements = the max elements that can be chosen without having the sum of any two being divisible by 3

CPhill Feb 8, 2019