2010 UNCO Math Contest II Problems/Problem 10
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Problem
Let where . What is the maximum number of elements in a subset of , which has at least three elements, such that for all in ? As an example, the subset of has the property that the sum of any two elements is strictly bigger than the third element, but the subset does not since is greater than . Since there is no subset of size satisfying these conditions, the answer for is .
Solution
if is even; if is odd.
See also
2010 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |