Difference between revisions of "2022 AIME II Problems/Problem 5"
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Twenty distinct points are marked on a circle and labeled <math>1</math> through <math>20</math> in clockwise order. A line segment is drawn between every pair of points whose labels differ by a prime number. Find the number of triangles formed whose vertices are among the original <math>20</math> points. | Twenty distinct points are marked on a circle and labeled <math>1</math> through <math>20</math> in clockwise order. A line segment is drawn between every pair of points whose labels differ by a prime number. Find the number of triangles formed whose vertices are among the original <math>20</math> points. | ||
| − | ==Solution== | + | ==Solution 1 == |
| + | |||
| + | Let <math>a</math>, <math>b</math>, and <math>c</math> be the vertex of a triangle that satisfies this problem, where <math>a</math> < <math>b</math> < <math>c</math>. | ||
| + | |||
| + | To be continued...... | ||
| + | |||
| + | ~[https://artofproblemsolving.com/wiki/index.php/User:Isabelchen isabelchen] | ||
==See Also== | ==See Also== | ||
{{AIME box|year=2022|n=II|num-b=4|num-a=6}} | {{AIME box|year=2022|n=II|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 04:45, 19 February 2022
Problem
Twenty distinct points are marked on a circle and labeled 
through 
in clockwise order. A line segment is drawn between every pair of points whose labels differ by a prime number. Find the number of triangles formed whose vertices are among the original points.
Solution 1
Let 
, 
, and 
be the vertex of a triangle that satisfies this problem, where < < .
To be continued......
See Also
| 2022 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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. 
