1992 AHSME Problems/Problem 23
==Problem== jj
Let be a subset of such that no pair of distinct elements in has a sum divisible by . What is the maximum number of elements in ?
Solution
The fact that is assumed as common knowledge in this answer.
First, note that there are possible numbers that are equivalent to , and there are possible numbers equivalent to each of -.
Second, note that there can be no pairs of numbers and such that mod , because then . These pairs are , , , and . Because is a pair, there can always be number equivalent to , and no more.
To maximize the amount of numbers in S, we will use number equivalent to , numbers equivalent to , and numbers equivalent to -. This is obvious if you think for a moment. Therefore the answer is numbers.
See also
1992 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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