Math Problem of the week#3

by Keith50, May 9, 2021, 6:53 AM

Math Problem of the week#3 wrote:
$\textbf{\color{blue}{AMC 12 2000/25:}}$ Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.) [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]
$ \textbf{(A)}\ 210 \qquad \textbf{(B)}\ 560 \qquad \textbf{(C)}\ 840 \qquad \textbf{(D)}\ 1260 \qquad \textbf{(E)}\ 1680$
Solution

A rising student who is always happy and striving for the best.

avatar

Keith50
Archives
Shouts
Submit
  • lovely blog!

    by llr, Apr 18, 2022, 1:41 AM

  • Great blog!
    Too advanced for me though :(

    by mathlearner2357, May 5, 2021, 2:13 PM

  • Hey, thanks for the shouts!

    by Keith50, Mar 19, 2021, 5:13 PM

  • cool blog!

    by hwdaniel, Mar 19, 2021, 4:54 PM

  • 2nd ! And the blog's CSS is really nice! Really nice blog!

    by jelena_ivanchic, Mar 11, 2021, 1:54 PM

  • first shout!!!!!

    by mobro, Dec 16, 2020, 5:25 AM

6 shouts
Tags
About Owner
  • Posts: 464
  • Joined: Dec 27, 2018
Blog Stats
  • Blog created: Aug 20, 2020
  • Total entries: 47
  • Total visits: 1990
  • Total comments: 4
Search Blog