Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 10"
m (moved 2010 UNC Math Contest II Problems/Problem 10 to 2010 UNCO Math Contest II Problems/Problem 10: disambiguation of University of Northern Colorado with University of North Carolina) |
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== Solution == | == Solution == | ||
| + | <math>\frac{n+2}{2}</math> if <math>n</math> is even; <math>\frac{n+1}{2}</math> if <math>n</math> is odd. | ||
== See also == | == See also == | ||
| − | {{ | + | {{UNCO Math Contest box|year=2010|n=II|num-b=9|num-a=11}} |
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Latest revision as of 01:57, 13 January 2019
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
if 
is even; 
if 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 | ||
