Difference between revisions of "1968 AHSME Problems/Problem 30"
m (→Solution 1) |
(→Solution 2) |
||
Line 14: | Line 14: | ||
== Solution 2 == | == Solution 2 == | ||
Try to get the answer experimentally. Draw two of the simplest shapes: a square and a triangle and maximize the number of intersections. You will discover it is 6, and the only expression provided that will give 6 is <math>\fbox{A}</math> | Try to get the answer experimentally. Draw two of the simplest shapes: a square and a triangle and maximize the number of intersections. You will discover it is 6, and the only expression provided that will give 6 is <math>\fbox{A}</math> | ||
+ | |||
+ | Note : this solution isn’t risk free, as the option of “None of These” is given as well. | ||
== See also == | == See also == |
Latest revision as of 06:50, 22 December 2020
Contents
Problem
Convex polygons and are drawn in the same plane with and sides, respectively, . If and do not have any line segment in common, then the maximum number of intersections of and is:
Solution 1
Notice how can pass through each line segment of at most twice. To have more than two intersections, the line passing through would have a zigzag shape which is impossible for convex polygons. Therefore, the intersections does not depend on and the answer is
Solution 2
Try to get the answer experimentally. Draw two of the simplest shapes: a square and a triangle and maximize the number of intersections. You will discover it is 6, and the only expression provided that will give 6 is
Note : this solution isn’t risk free, as the option of “None of These” is given as well.
See also
1968 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 29 |
Followed by Problem 31 | |
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.