2012 AMC 12A Problems/Problem 17
Problem
Let be a subset of with the property that no pair of distinct elements in has a sum divisible by . What is the largest possible size of ?
Solution
Of the integers from to , there are six each of . We can create several rules to follow for the elements in subset . No element can be if there is an element that is . No element can be if there is an element that is . Thus we can pick 6 elements from either or and 6 elements from either or for a total of elements. Considering , there can be one element that is so because it will only be divisible by if paired with another element that is . The final answer is .
Video Solution by OmegaLearn
https://youtu.be/orrw4VydBTk?t=483
~ pi_is_3.14
See Also
2012 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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