Difference between revisions of "2017 AIME II Problems/Problem 13"
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| − | + | ==Problem== | |
For each integer <math>n\geq3</math>, let <math>f(n)</math> be the number of <math>3</math>-element subsets of the vertices of the regular <math>n</math>-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of <math>n</math> such that <math>f(n+1)=f(n)+78</math>. | For each integer <math>n\geq3</math>, let <math>f(n)</math> be the number of <math>3</math>-element subsets of the vertices of the regular <math>n</math>-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of <math>n</math> such that <math>f(n+1)=f(n)+78</math>. | ||
| − | + | ==Solution== | |
<math>\boxed{245}</math> | <math>\boxed{245}</math> | ||
| + | |||
| + | =See Also= | ||
| + | {{AIME box|year=2017|n=II|num-b=12|num-a=14}} | ||
| + | {{MAA Notice}} | ||
Revision as of 13:01, 23 March 2017
Problem
For each integer 
, let 
be the number of 
-element subsets of the vertices of the regular 
-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of such that 
.
Solution
See Also
| 2017 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
