Mark:
CUBE
I think there are 27! * 24^27 ways to reconstruct the cube.
I think there are:
1! * 24^1 ways to get the center cube correct
6! * 4^6 ways to get the centers of the faces correct
8! * 3^8 ways to get the corners correct
12! * 2^12 ways to get the edges correct
That gives us:
(1! * 24^1 * 6! * 4^6 * 8! * 3^8 * 12! * 2^12) / (27! * 24^27)
which is approximately:
1.8298 * 10^(-37)
Way to go dude!
This problem is a counting exercise. We will count the number of cube orientations and arrangements such that the outside of the larger cube is black, and then divide this by the total number of possible orientations and arrangements to obtain the required probability.
We will count without any consideration of symmetry. Other counting methods could be used, but as long as we are consistent we will obtain the correct probability.
Consider the four types of cubes upon disassembly:
a. 8 cubes with three faces painted black;
b. 12 cubes with two black faces;
c. 6 cubes with one black face;
d. 1 completely white cube.
Each cube of type (a) must be oriented in one of three ways, giving 3^8 possible orientations. Next, each corner cube must be placed in one of eight corners, giving 8! possible arrangements. Thus we have 3^8 8! possibilities in all.
Similarly, each cube of type (b) must be oriented in one of two ways, giving 2^12 possible orientations. Then, each edge cube must go to one of 12 edges, giving 12! possible arrangements. Thus we have 2^12 12! possibilities in all.
Also, each cube of type (c) has four possible orientations, and may be placed in one of six positions, yielding 4^6 6! possibilities.
Finally, the one white cube of type (d) may be oriented in 24 ways. (Four ways for each face.)
Thus the total number of correct reassemblings is a = 3^8 8! 2^12 12! 4^6 6! 24.
To find the total number of possible reassemblings, consider that each cube may be oriented in 24 ways, and there are 27! possible arrangements of the cubes, giving b = 24^27 27! possibilities in all.
Therefore, the probability that the outside of the reassembled cube is completely black is:
a/b = 1/(2^56 3^22 5^2 7 11 13^2 17 19 23) = 1/5465062811999459151238583897240371200 1.83 ?- 10−^37.
QUESTION:
If you multiply 3 counting numbers together then what percentage of the answers is divisible by 10?
I get something close to 50%
Slippy writes, "
Oh yeah, I agree with TTH
"
I fear you are too late; she may have left for good this time!
QUESTION:
A E I O U Y
Why is O the odd one out?
Odd One Out
Listen to our little song
It doesn't matter if you don't belong
So don't worry if you have to shout
Looks like I'm the odd one out
Everyday whatever you play
Someone's not going to fit
So if it's you then don't feel blue
It doesn't matter one little bit
No it doesn't
Listen to our little song
It doesn't matter if you don't belong
So don't worry if you have to shout
Looks like I'm the odd one out
It really isn't all that bad
Don't let it make you feel mad
So when it's you just laugh and say
I'm gonna find something else to play
Listen to our little song
It doesn't matter if you don't belong
We want you to sing and shout
I like being the odd one out
I like being the odd one out
Listen to our little song
It doesn't matter if you don't belong
So don't worry if you have to shout
Looks like I'm the odd one out
Everyday whatever you play
Someone's not going to fit
So if it's you then don't feel blue
It doesn't matter one little bit
No it doesn't
Listen to our little song
It doesn't matter if you don't belong
So don't worry if you have to shout
Looks like I'm the odd one out
It really isn't all that bad
Don't let it make you feel mad
So when it's you just laugh and say
I'm gonna find something else to play
Listen to our little song
It doesn't matter if you don't belong
We want you to sing and shout
I like being the odd one out
I like being the odd one out
"
too many probability questions."
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Most people are sceptical when I tell them I can calculate any six digit number they choose! If I fail; you get 10 bucks; if you loose; I get one dollar.
So this is the deal
..
Write down any three-digit number (genuinely three digits, ie, not beginning with 0), then write it down again, so as to give a 6-digit number, for example 123123.
Divide the six-digit number by 7.
Next, divide the answer by 11.
Next, divide that answer by 13 (Don't worry about the remainder; there won't be one.)
Recognise the number
Holy moly; choose a different three numbers
How many times does the letter F(or f) appear in the following item
Finished files are the
result of years of scientific
study combined with the
experience of years.
(Sorry Missmi; it isn't eleventeen).
