|
|
|
Go 
|
Post 
|
Find 
|
Notify 
|
|
Reply 
|
|
Admin 
|
New PM! 
|
Platinum Enthusiast
|
I'm just as confused as frankvan about the given problem. If this is about the possible shapes of a convex (or concave?) polyhedron with 8 faces, then more info is needed.
On the other hand, if this is about a box with pictures on 8 sides, ignoring the top and bottom, then it is equivalent to asking how many distinct ways 8 guests may be seated at a round dinner table, not counting rotations of the table. The answer is 7! (7-factorial) = 7*6*...*2*1 = 5,040.
|
| |
|
Diamond Enthusiast

|
Are the sides otherwise distinguishable? I would guess they are not, in which case the answer would be less than 8-factorial (how much less, I'm not sure).
|
| |
|
Diamond Enthusiast

|
Tried to edit, but I apparently timed out. A more complete reply with a partial thinking through:
Are the sides otherwise distinguishable?
If they are, Pin~Jinx is correct.
I would guess, however, they they are not. In that case, you would need a correction factor to account for arrangements that are only rotations of other arrangements. For a round table with 8 seats, the correction would be to divide by the number of seats. That is 8!/8 = 7!, which is the answer Professor gave. However, I'm not sure that 8 is the appropriate factor for an 8-sided object. For the 8-sided object, you can rotate to 4 positions horizontally and to 4 positions vertically. I think those need to be multiplied rather than added (that is, I think there are 4 vertical rotations for each of the 4 horizontal rotations). That would give 8!/(4*4) = 2520.
I may be completely off about that, and I don't think I'm being particularly clear, but I thought I should put in my two cents, and I don't have time for three at the moment. Maybe Prof. and Pin~jinx can sort out if what I'm saying is correct and can better explain it.
|
| |
|
Platinum Enthusiast
|
methos, are you picturing this box as an octahedron? My image is of an octagonal prism, the end faces (top and bottom) of which are ignored. Another possibility is a hexagonal prism with the end faces counting, in which case there are (8*7/2!)*(5!)*2 = 6,720 permutations.
The fact is, we need the original questioner to explain what was meant by "a box that has 8 sides."
|
| |
|
Diamond Enthusiast

|
Yes, I was picturing an octahedron (I missed your comment about ignoring the top and bottom)... something like: You're right that we need more info. Even if it's an octagonal prism, now that I think about it, it matters whether or not the top and bottom are interchangeable. If not, I'd agree with 8!. If so, I think it would be 8!/2.
|
| |
|
 | Please Wait. Your request is being processed... |
© 2002-2010 AnswerPool.com
All Rights Reserved
Using This Site Means You Accept Its Terms of Service and Privacy Policy
Close Cover Before Striking
3D Glasses Required for Optimal Viewing
Now in HD and Surround Sound
Offer Void Where Prohibited by Law
There's a Bathroom on the Right
Caution - Objects May Be Closer Than They Appear
Anything You Post May Be Used Against You in the Court of Public Opinion
Notice: All Employees and Customers Are Required to Wash Their Hands and Feet Before Posting by the Board of Health
Visit DiscussionPool.com! |