A number of long, thin sticks are lying in a pile at odd angles such that the sticks cross each other.
a) Relate the maximum number of intersection points of n sticks to entries
in Pascal’s triangle.
b) What is the maximum number of intersection points with six overlapping sticks?
2006-11-15 16:24:00 · 3 answers · asked by ravi l 1 in Science & Mathematics ➔ Mathematics
This is a permutation combination math.
For maximum intersection, no two sticks are parallel.
2 sticks can have 1 intersection
a third stick can intersect with 2 other sticks
so, 3 sticks can have 1+2 intersection = 3
a fourth stick can intersect with 3 other sticks
so, 4 sticks can have 1+2+3 intersection = 6
a fifth stick can intersect with 4 other sticks
so, 5 sticks can have 1+2+3+4 intersection = 10
So n+1 sticks can have 1+2+3+...+n intersections or n(n+1)/2
so n sticks have n(n-1)/2 intersections
b) 6 sticks can have max 6*5/2 = 15 intersections
2006-11-16 00:27:29 · answer #1 · answered by The Potter Boy 3 · 0⤊ 0⤋
www.doyourownhomework.com
2006-11-15 16:55:10 · answer #2 · answered by sweetsomething2003 2 · 0⤊ 0⤋
Twelve...............................................................................(?)
2006-11-15 16:37:30 · answer #3 · answered by Anonymous · 1⤊ 0⤋