Difference between revisions of "2019 AMC 10A Problems/Problem 14"
(Created page with "{{duplicate|2019 AMC 10A #14 and 2019 AMC 12A #8}} For a set of four distinct lines in a plane, there are exactly <math>N<...") |
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==Solution== | ==Solution== | ||
| + | Drawing <math>4</math> lines, you see that the maximum points of intersection is <math>6</math>. Then, we see that we can not make <math>5</math> intersection points and can just make a quadrilateral, triangle, two T's, and one pair of coordinate axis to make <math>4,3,2,</math> and <math>1</math> points of intersection. Thus the answer is <math>1+2+3+4+6</math> to get <math>16, B</math> | ||
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| + | -Lcz | ||
==See Also== | ==See Also== | ||
Revision as of 17:35, 9 February 2019
- The following problem is from both the 2019 AMC 10A #14 and 2019 AMC 12A #8, so both problems redirect to this page.
For a set of four distinct lines in a plane, there are exactly 
distinct points that lie on two or more of the lines. What is the sum of all possible values of ?
Solution
Drawing 
lines, you see that the maximum points of intersection is 
. Then, we see that we can not make 
intersection points and can just make a quadrilateral, triangle, two T's, and one pair of coordinate axis to make 
and 
points of intersection. Thus the answer is 
to get 
-Lcz
See Also
| 2019 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2019 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
