Triangular Cubes (Posted on 2004-12-04)

	Submitted by Erik O.
Rating: 3.0000 (2 votes)
Solution:	(Hide)
The first step in solving this problem is to figure out how many different triangles can be made using the vertices of a cube. Since there are 8 vertices, the first point can be picked from one of 8 vertices, the second point can be picked from the 7 remaining vertices, and the last point of the triangle can be picked from the 6 remaining vertices. There are, therefore, 8𡥚 = 336 ways to draw a triangle on (or inside) a cube, when you disregard the sequence of choosing points for the triangles. Taking the point sequence into account, we can divide 336 by 6 to come up with 56 unique triangles. Of those 56 triangles, only 8 are regular triangles. To draw a regular triangle in a cube, the first two points must fall on opposing diagonals of a single face. The last point is taken from one of the two points on the opposite face on a corner that does not share an edge with the first two points. The remaining triangles are all right triangles. Therefore the probability of getting a regular triangle is 8/56 = 1/7 = 0.14286..., and the probability of getting a right triangle is 48/56 = 6/7 = 0.85714...

	Subject	Author	Date
	Triangulars cubes REVISITED	Ady TZIDON	2010-08-16 14:02:38
	Answer	K Sengupta	2008-03-15 03:42:16
	re(2): i c it this way	Ady TZIDON	2004-12-07 09:41:36
	re: Same answer, different approach	owl	2004-12-06 15:01:01
	Same answer, different approach	nikki	2004-12-06 14:16:01
	The way I did it (statistical)	Larry	2004-12-06 03:23:49
	re: i c it this way	Charlie	2004-12-05 15:15:44
	i c it this way	Ady TZIDON	2004-12-05 07:53:06
	Geometry... It's been too long	Dustin	2004-12-05 02:58:48
	Solution	Steve Herman	2004-12-04 17:25:13
	Solution	Bractals	2004-12-04 17:21:28