Ok, first to answer correctly, with a solution that is both succint and clear gets my best answer vote.
Okay, let's get started:
Eight points on a circle are grouped into disjoint pairs. Each pair is joined by a chord. Find the number of ways of joining the pairs such that no two of the chords intersect.
2007-01-14 00:39:30 · 4 answers · asked by Sentient 2 in Science & Mathematics ➔ Mathematics
We count according to the number of pairs where the points are neighbours.
If there are 4 such pairs, then there is 2 possibilities. (Obvious).
If there are 3 such pairs, then one of them separates the 3 pairs in
2 on one side and 1 on the other side. Any chord where the "distance" between the end points is 3 is going to give exactly one such configuration. There are 8 such chords. So 2+8=10 so far.
If there are 2 such pairs, then the 2 pairs that don't have "length" 1 must have length 3. So it is easy to see that if the points are in a regular octogone, all the chords are parallel, and there are 4 possible directions.
It is not possible that there is no such pair. So the total is 14... if I am not mistaken.
2007-01-14 01:05:44 · answer #1 · answered by gianlino 7 · 0⤊ 0⤋
the reply is 40 2. enable's call both numbers A and B. all of us recognize that each and each of the numbers is divisible by using 6. So, enable's outline 2 further numbers: "little a" a = A/6 ? A = 6 * a "little b" b = B/6 ? B = 6 * b 504 = A * B = 6 * a * 6 * b = 36 * a * b a * b = 504/36 = 14 14 will be factored as a million * 14 or 2 * 7. when you consider that neither A nor B is precisely 6, neither a nor b will be precisely a million. So, a and b are 2 and seven. A and B are 2 * 6 and seven * 6. both huge style are 12 and 40 2. you are able to ascertain that those are each and each divisible by using 6, and their product is 504. the more suitable of both is 40 2.
2016-10-31 01:50:59 · answer #2 · answered by Anonymous · 0⤊ 0⤋
There are 2 ways to connect 8 points on a circle into 4 disjoint pairs (whose cords do not intersect). As each point can have two nearest neighbors. There are another 2 ways (horizontally & verically) to connect non intersecting cords for pairs of points which connect two points who have in between them 1 and 2 pairs of points. The total number is therefore 16 = (8*2*2)/2
2007-01-14 01:30:38 · answer #3 · answered by Boehme, J 2 · 0⤊ 1⤋
2OR0
2007-01-14 00:45:46 · answer #4 · answered by SAI H 2 · 0⤊ 1⤋