Math Problem of the week#3
by Keith50, May 9, 2021, 6:53 AM
Math Problem of the week#3 wrote:

![[asy]import three;
import math;
size(180);
defaultpen(linewidth(.8pt));
currentprojection=orthographic(2,0.2,1);
triple A=(0,0,1);
triple B=(sqrt(2)/2,sqrt(2)/2,0);
triple C=(sqrt(2)/2,-sqrt(2)/2,0);
triple D=(-sqrt(2)/2,-sqrt(2)/2,0);
triple E=(-sqrt(2)/2,sqrt(2)/2,0);
triple F=(0,0,-1);
draw(A--B--E--cycle);
draw(A--C--D--cycle);
draw(F--C--B--cycle);
draw(F--D--E--cycle,dotted+linewidth(0.7));[/asy]](http://latex.artofproblemsolving.com/c/8/e/c8ed0e44f14320ddf90acf550ca4ea2c7066b98d.png)

Given that there are
symmetries in a regular octahedron, (there are
ways of choosing the top vertex and
ways to rotate it) and there are
ways of arranging the colours, there are
distinguishable ways.




