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![[Post New]](/templates/default/images/icon_minipost_new.gif) 16 May 2008 17:56:34 IST
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In how many ways can cube be painted with 6 different colours
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16 May 2008 19:37:56 IST
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6^6 ways each side has six options(provided each side is painted with 1 colour)
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16 May 2008 19:42:30 IST
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no 6^6 is definitely wrong because faces of a cube r identical
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"Imagination is more important than knowledge."
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16 May 2008 19:46:11 IST
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i think its 6^6 even though every side is identical but the faces are different..
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16 May 2008 20:28:36 IST
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by sides i meant to say that faces are identical
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16 May 2008 20:31:48 IST
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if all colours have to be used(an assumption by me) then
colouring will vary only when two opoosite pair of faces have different colours
so two make three differnt pairs out of 6
no .of ways = (6C2 * 4C2)/3 = 90/3 = 30
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16 May 2008 21:03:29 IST
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6^5?
6^6 because there are six available choices and divide by 6 because all faces are identical?
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16 May 2008 21:08:19 IST
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is it 6! ways bcause ...the rel position of colours only matter...,,now consider one colour....fix it to one side..now others u can do in 5*4*3*2*1..now the no. of colours to fix are 6...thus answer is 6*5!...correct if i am wrong...
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16 May 2008 21:09:42 IST
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It's not been mentioned that you've to use a colour only once..
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16 May 2008 21:11:31 IST
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oh!! in tht case.....it must be 6^6 .....
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The only place where you will find success before hard work is in the dictionary
A winner never quits.....a quitter never wins......
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16 May 2008 21:14:57 IST
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moreover they didnt mention colours can be repeated....well question is incomplete...so wat is finally the correct answer.?
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The only place where you will find success before hard work is in the dictionary
A winner never quits.....a quitter never wins......
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16 May 2008 21:15:02 IST
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But then again all six sides are identical so if you rotate it one way, you get the same configuration again.
I think it's 6C3.6C3
First you choose three non-opposite sides.. Then you coat them with three colours. Now you choose three colours for the other three sides. This way uniqueness is maintained in opposing sides.
Is that ok?
Can't think clearly at all at the moment..
Watching IPL..
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16 May 2008 21:53:37 IST
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Thirty. Always put the green face on the table. (a) If the red face is now on top, you can always turn the yellow face towards you; then three faces remain to be coloured, in 3.2.1 = 6 ways. (b) If the red face is not on top, then turn it towards you and then four faces remain to be coloured, in 4.3.2.1 = 24 ways
I an sure of this ans 
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16 May 2008 22:49:16 IST
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The above ans is when the colours are not repeated
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Hard Work Pays !
Good Luck to ALL !!
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17 May 2008 09:44:37 IST
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