Home » Ask & Discuss » Mathematics. » Algebra « Back to Discussion

Algebra

Blazing goIITian

Joined:	13 Jul 2008
Post:	382

13 Apr 2009 23:15:08 IST

0 People liked this

1489

A very good Question

None

In how many ways can 6 faces of a cube be painted with 6 different colours????

Please explain the answer also..

Share this article on:

Comments (34)

Go to Page...

STONE COLD RATTLESNAKE

Blazing goIITian

Joined: 15 Jul 2008

Posts: 315

13 Apr 2009 23:23:44 IST

Like 1 people liked this

6!*6!+5!/2 Is it correct. Verify

STONE COLD RATTLESNAKE

Blazing goIITian

Joined: 15 Jul 2008

Posts: 315

13 Apr 2009 23:24:37 IST

Like 0 people liked this

this is very conceptual question, u can find the anser in rd sharma objective.

Rohit

Blazing goIITian

Joined: 13 Jul 2008

Posts: 382

13 Apr 2009 23:33:42 IST

Like 0 people liked this

No,that's not the right answer.

Aditya

Blazing goIITian

Joined: 4 Feb 2008

Posts: 590

13 Apr 2009 23:45:08 IST

Like 0 people liked this

it should be one........

Rohit

Blazing goIITian

Joined: 13 Jul 2008

Posts: 382

14 Apr 2009 00:16:34 IST

Like 0 people liked this

I'm damn sure that 1 can't be the answer.For example,blue is opp. to green and then opp. to red,both cases are different...

Rohit

Blazing goIITian

Joined: 13 Jul 2008

Posts: 382

14 Apr 2009 12:02:16 IST

Like 0 people liked this

More views please....

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

Posts: 5517

14 Apr 2009 12:07:10 IST

Like 0 people liked this

posted the correct answer ...scroll down

Soumik

Blazing goIITian

Joined: 31 Jul 2008

Posts: 1266

14 Apr 2009 12:24:12 IST

Like 0 people liked this

Lay the cube flat with all its sides open on the floor facing u......now analyse it.

It's easier that way.

Siddhartha Gupta

Blazing goIITian

Joined: 1 Nov 2008

Posts: 329

14 Apr 2009 12:29:22 IST

Like 1 people liked this

shouldn't it be 6^6 ie 6×6×6×6×6×6

bharat goswami

Blazing goIITian

Joined: 9 Mar 2008

Posts: 592

14 Apr 2009 12:37:48 IST

Like 0 people liked this

i think ans. is 2880..

swapnil joshi

Blazing goIITian

Joined: 10 Apr 2009

Posts: 466

14 Apr 2009 12:43:57 IST

Like 0 people liked this

since number of colors r specifiedand also no of sideso we have solution as 6P6=6factorial=720 ways

Rohit

Blazing goIITian

Joined: 13 Jul 2008

Posts: 382

14 Apr 2009 13:23:13 IST

Like 0 people liked this

The answer is between 0 to 60 only..

Swapnika.... finally into a branded college....NIT m cuming..!!!

Blazing goIITian

Joined: 7 Aug 2008

Posts: 1047

14 Apr 2009 13:25:27 IST

Like 0 people liked this

how can it b only 0-60...u hav 6 faces and 6 colors...!!!!!....it shud b 6^6...i.e. 6x6x6x6x6x6

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

Posts: 5517

14 Apr 2009 13:27:03 IST

Like 2 people liked this

I guess there is a simpler solution . Let us look at any combination so that we always face the side painted with the same color (say, red). In this case we have 5 sides left, therefore there is 5! = 120 ways to paint other 5 sides.
Now the uniqueness comes into play. Still holding the cube facing the selected (red) side, just rotating it around the axis, perpendicular to this selected side, we can put it in 4 different orientations, obviously repeating each other. THerefore we have to consider only one out of orientations, and the number of solutions is 5!/4 = 120/4=30

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

Posts: 5517

14 Apr 2009 13:28:23 IST

Like 1 people liked this

rohit's post gave me the idea.

Rohit

Blazing goIITian

Joined: 13 Jul 2008

Posts: 382

14 Apr 2009 13:32:38 IST

Like 0 people liked this

The answer that i have is even smaller,but i don't trust it..So lets see what others say,but i liked nugorama bhaiyya's explanation.

Swapnika.... finally into a branded college....NIT m cuming..!!!

Blazing goIITian

Joined: 7 Aug 2008

Posts: 1047

14 Apr 2009 13:33:18 IST

Like 0 people liked this

may b he is right...

akash roy

New kid on the Block

Joined: 14 Apr 2009

Posts: 2

14 Apr 2009 14:23:05 IST

Like 1 people liked this

the ans is 21

AViK

Blazing goIITian

Joined: 5 Sep 2008

Posts: 953

14 Apr 2009 21:04:16 IST

Like 1 people liked this

Even i get it as 30....

say colours are P Q R S T U

let ny sides 1 & 2 (opp. sides) be painted with colours P & Q

so v are left with 4 sides n 4 colours so ways = 4!

but notice tht v can rotate it either way 2 get similar orientations...

like RSTU ...STUR.... TURS ....RSTU (going in order) wud mean the same..

so ways fr the 4 sides = 4!/4 = 3! (v cud also hav considered circular PnC directly fr this!)

now if v keep ny one fixed (eg P on side 1) side 2 can hav "5" choices....according 2 which rest of the 4 colours wud b arranged...

So total ways = 5*3! = 30 ways...

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team