Difference between revisions of "1992 AHSME Problems/Problem 22"
(Created page with "== Problem == Ten points are selected on the positive <math>x</math>-axis,<math>X^+</math>, and five points are selected on the positive <math>y</math>-axis,<math>Y^+</math>. Th...") |
(Added a solution with explanation) |
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== Solution == | == Solution == | ||
| − | <math>\fbox{B}</math> | + | <math>\fbox{B}</math> We can pick any two points on the <math>x</math>-axis and any two points on the <math>y</math>-axis to form a quadrilateral, and the intersection of its diagonals will thus definitely be inside the first quadrant. Hence the answer is <math>10C2 \times 5C2 = 450</math>. |
== See also == | == See also == | ||
Latest revision as of 02:05, 20 February 2018
Problem
Ten points are selected on the positive 
-axis,
, and five points are selected on the positive 
-axis,
. The fifty segments connecting the ten points on to the five points on are drawn. What is the maximum possible number of points of intersection of these fifty segments that could lie in the interior of the first quadrant?
Solution
We can pick any two points on the -axis and any two points on the -axis to form a quadrilateral, and the intersection of its diagonals will thus definitely be inside the first quadrant. Hence the answer is 
.
See also
| 1992 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
