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Updated on: 13 Aug 2003, 08:33
Originally posted by AkamaiBrah on 12 Aug 2003, 06:35.
Last edited by AkamaiBrah on 13 Aug 2003, 08:33, edited 1 time in total.
Last edited by AkamaiBrah on 13 Aug 2003, 08:33, edited 1 time in total.
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You have 12 colors of paint. How many *distinct* ways can you paint a regular dodecahedron (12-sided 3-d figure) using all 12 colors, one color to a side. (If you can rotate a painted dodecahedron in a manner so that it looks like another painted one, they are the same and not distinct).
Recall a regular dodecahedron has a pentagon on top, one on the bottom and two row of 5 pentagons each in the middle. (if you play D&D, you know what they look like).
You can leave it in combined factorial and/or combinatorial form if desired.
This seems dauntingly complex but is really easy if you understand the method. (I will give at least 3 solutions).
Recall a regular dodecahedron has a pentagon on top, one on the bottom and two row of 5 pentagons each in the middle. (if you play D&D, you know what they look like).
You can leave it in combined factorial and/or combinatorial form if desired.
This seems dauntingly complex but is really easy if you understand the method. (I will give at least 3 solutions).
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12 Aug 2003, 07:13
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mciatto
AkamaiBrah
You have 12 colors of paint. How many *distinct* ways can you paint a regular dodecahedron (12-sided 3-d figure) using all 12 colors, one color to a side. (If you can rotate a painted dodecahedron in a manner so that it looks like another painted one, they are the same and not distinct).
Recall a regular dodecahedron has a pentagon on top, one on the bottom and two row of 5 pentagons each in the middle. (if you play D&D, you know what they look like).
You can leave it in combined factorial and/or combinatorial form if desired.
This seems dauntingly complex but is really easy if you understand the method. (I will give at least 3 solutions).
Recall a regular dodecahedron has a pentagon on top, one on the bottom and two row of 5 pentagons each in the middle. (if you play D&D, you know what they look like).
You can leave it in combined factorial and/or combinatorial form if desired.
This seems dauntingly complex but is really easy if you understand the method. (I will give at least 3 solutions).
12 * 9!
If you explain your logic I can tell you where you messed up.
12 Aug 2003, 07:18
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AkamaiBrah
mciatto
AkamaiBrah
You have 12 colors of paint. How many *distinct* ways can you paint a regular dodecahedron (12-sided 3-d figure) using all 12 colors, one color to a side. (If you can rotate a painted dodecahedron in a manner so that it looks like another painted one, they are the same and not distinct).
Recall a regular dodecahedron has a pentagon on top, one on the bottom and two row of 5 pentagons each in the middle. (if you play D&D, you know what they look like).
You can leave it in combined factorial and/or combinatorial form if desired.
This seems dauntingly complex but is really easy if you understand the method. (I will give at least 3 solutions).
Hint: recall this problem
https://www.gmatclub.com/phpbb/viewtopic.php?t=1574
Recall a regular dodecahedron has a pentagon on top, one on the bottom and two row of 5 pentagons each in the middle. (if you play D&D, you know what they look like).
You can leave it in combined factorial and/or combinatorial form if desired.
This seems dauntingly complex but is really easy if you understand the method. (I will give at least 3 solutions).
Hint: recall this problem
https://www.gmatclub.com/phpbb/viewtopic.php?t=1574
12 * 9!
If you explain your logic I can tell you where you messed up.
OOPS, I will change my answer to 11 * 9!
I fixed the top side, leaving 11 possibilities for the bottom. Now there are 10 sides in the "middle". For these, from what I have learned in your last post dealing with the cube there are (n-1)! (makes sense because you hold one of them constant and rotate all others) So (10-1)! = 9!
Final Answer 11 * 9!.
