Difference between revisions of "2012 AMC 12A Problems/Problem 17"
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Revision as of 08:57, 4 July 2013
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 
iff there is an element that is 
. No element can be 
iff there is an element that is 
. Ignoring those that are 
, we can get a subset with 
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 
.
See Also
| 2012 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 16 |
Followed by Problem 18 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
