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.
+128407 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
