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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.

 Feb 8, 2019
 #1
avatar+98129 
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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

 

 

 

 

 

cool cool cool

 Feb 8, 2019
edited by CPhill  Feb 8, 2019
edited by CPhill  Feb 8, 2019
 #2
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thank you, but could you explain what you did? 

Guest Feb 8, 2019
 #3
avatar+98129 
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See my  corrected answer....I hope it is clear...

 

 

cool cool  cool

CPhill  Feb 8, 2019

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