Difference between revisions of "2023 AIME I Problems/Problem 3"
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| − | Unofficial problem statement: In a plane there exists <math>40</math> lines, none of which are parallel. There are <math>3</math> points in which exactly <math>3</math> lines intersect, <math>4</math> points in which exactly <math>4</math> lines intersect, <math>5</math> points in which exactly <math>5</math> lines intersect, and <math>6</math> points in which exactly <math>6</math> lines intersect. There are no points in which more than <math>6</math> lines intersect. How many points are there in which exactly <math>2</math> lines intersect? | + | Unofficial problem statement: |
| + | In a plane there exists <math>40</math> lines, none of which are parallel. There are <math>3</math> points in which exactly <math>3</math> lines intersect, <math>4</math> points in which exactly <math>4</math> lines intersect, <math>5</math> points in which exactly <math>5</math> lines intersect, and <math>6</math> points in which exactly <math>6</math> lines intersect. There are no points in which more than <math>6</math> lines intersect. How many points are there in which exactly <math>2</math> lines intersect? | ||
Revision as of 12:56, 8 February 2023
Unofficial problem statement:
In a plane there exists 
lines, none of which are parallel. There are 
points in which exactly lines intersect, 
points in which exactly lines intersect, 
points in which exactly lines intersect, and 
points in which exactly lines intersect. There are no points in which more than lines intersect. How many points are there in which exactly 
lines intersect?
