24I am writing something for which Nishant sir wil kill me [3]
Polya's Enumeration Formula for the cube is:
1/24 * (c6 + 3*c4 + 12*c3 + 8*c2)
where c is the number of colors
In how many ways can you color a cube with
a) one color
b) two colors
c) three colors
d) 4 colors
e) 5 colors
f) 6 colors
Each of them is easy ... just needs a bit of thinking :)
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42 Answers
2424kkk
btw i am trying the question from basics too
(following ur advice [1])
1is the answer for 2 colors 7
the rest are becoming a bit lengthy
62I dont think too many of these wud be lengthy if you could visualize..
THe problem could be to explain this one on a forum in text :P
1for 2 colors
2 ways when we use 1 color for only one face
4 ways when we use 1 color for only two faces
1 ways when we use 1 color for only three faces
but the formula gives answer as 10
3hey injun i think we cant take the qn as an anology of a dice.becos here all the faces are identical,but in a dice all are distinct.
1But we make them distinct by numbering them in different order!!
We can surely do so by painting them!
1@ Nishant bhaiyya
if there are two colors only say 1 and 2
we can use color 1 on one face and color 2 for rest five
and...... vice versa ... all other positionings in which one of the colours is used for only one face should be identical [7]
39cool discussion going on!!
because o exam i am missing a lot over here :(
24u cna see the hidden contetn too dude if u like..
anyways for u again writing that
Polya's Enumeration Formula for the cube is:
1/24 * (c6 + 3*c4 + 12*c3 + 8*c2)
where c is the number of colors
3is there ne restriction that is can we colour each side with one colour. or can we colour more than one colour for each side.
