[Math4u] Re: Cube problem

Question 1
I agree with Jim's answer. There are 6 color choices for one square
and 5 remaining color choices for the opposite square. But the cube
can be flipped over causing half the choices to be duplicates. So
the answer is 6*5/2=15
Question 2
First of all we chose 4 colors out of 6 different colors.
I get 6*5*4*3=360.
Let's chose two colors to exclude:
I get 6*5=30
What a discrepancy! We should get the same answer picking 4 colors
or excluding 2 colors.
Obviously, if we chose 6 colors out of six different colors, there is
only one possibility. So we must chose the lower number. There are
30 different ways to choose 4 colors out of 6.
Let's call these colors 1,2,3,and 4.
These 4 colors are to be arranged in a band around the cube. One of
the sides will have color 1. There are three remaining colors to
choose from to be opposite color 1.
So I'd say the answer is 30*3=90.
Question 3
We have a cube colored with 6 colors.
There are 5 choices for the color opposite color 1. Let's call the
remaining colors 3,4,5,and 6. Color 3 will be between the first two
colors.
There are 3 choices for the color opposite color 3.
There are 2 remaining choices for arranging the last 2 colors.
So I'd say the answer is 5*3*2=30
Regards,
Brian

--- In Math4u@yahoogroups.com, "sanjivadayal" <sanjivadayal@...>
wrote:
>
> Question:-
> Given six different colours and a cube.
> 1. In how many ways two opposite faces of the cube can
> be coloured with two different colours?
> 2. In how many ways four faces of the cube can be
> coloured with four different colours of which two
> faces are opposite and other two faces are also
> opposite?
> 3. In how many ways all six faces of the cube can be
> coloured with six different colours?
>

Yahoo! Groups Links

<*> To visit your group on the web, go to:

http://groups.yahoo.com/group/Math4u/

<*> Your email settings:
Individual Email | Traditional

<*> To change settings online go to:

http://groups.yahoo.com/group/Math4u/join

(Yahoo! ID required)

<*> To change settings via email:
mailto:Math4u-digest@yahoogroups.com
mailto:Math4u-fullfeatured@yahoogroups.com

<*> To unsubscribe from this group, send an email to:
Math4u-unsubscribe@yahoogroups.com

<*> Your use of Yahoo! Groups is subject to:

http://docs.yahoo.com/info/terms/