Help!Extremely confusing homework question?

Question

I need help with this homework question
Ive never been good at math and I am absolutley
bazzled at this question I dont' get it at all
can some1 please tell me how I might figure it out
or what the answer is
here is the question exactly as written:

Mrs. Jones had some white paint and some green paint, and a bunch of wooden cubes. Her class decided to paint the cubes by making each face either solid white or green.
Jaun painted his cube with all 6 faces white--Julie painted her cube solid green. Hector painted four faces white and 2 faces green. How many cubes could be painted in the fashion, so that each cube is different from the others? Two cubes are alike if one can be turned so that it exactly matches, color for color on each side, the other cube.

Pleeeeez help i will except all answers just try pleeeez.

Answer 1

Okay, so I'm assuming what the question means is that you have to find the number of cubes you can make with any combination of green and white sides.

I think that the best way to solve this problem would be to draw it out on paper.

I drew each cube (as a series of four squares in the form of a cross) and separated them into groups of how many green sides (one green side, two green sides, etc.). You could do number of white sides if you want.

Key: w = white side
g = green side

0 Green Sides:
one combination
all sides white
w
w w w
w
w

1 Green Side:
one combination
one green side anywhere
w
w g w
w
w

2 Green Sides:
two combinations
w
g w g
w
w
and
g
w g w
w
w

3 Green Sides:
two combinations
g
w g w
g
w
and
w
g g w
g
w

4 Green Sides:
two combinations
g
w g w
g
g
and
g
g g g
w
w

5 Green Sides:
one combination
one white side anywhere
g
g w g
g
g

6 Green Sides:
one combination
all sides green
g
g g g
g
g

So all together there are 10 different combinations to place green and white sides so that no two cubes are identical.

Hope that helped.

Answer 2

There are only 2 full solid colour cubes. You know that because there are only 2 colours. Now here's a list for the amount of green/white there could be on each cube. Green- 1 Green 5 White, 2 Green 4 White, 3 Green3 White. White- 1 White 5 Green, 2 White 4 Green. Now the only thing that's difficult with this problem is that you can put them in different orders. The cube is a 6 sided 3D geometrical figure, but if you put things in a different order, chances are they will look the same after every few combinations. You can only make 2 combinations of colour with 2 and 4 of whatever, because there are 2 cubes with that colour scheme (one dominated by white, and the other by green) equaling to 4 total. So to simply put it, there are only 8 different possible cubes.

Answer 3

Bazzled? Interesting word choice.

For each cube, there are 6 faces. Each face is entirely white or entirely green. Let w=# of white faces and g=# of green faces. You have two options by painting each side either white or green. That is (w,g)=(6,0) -> 1, and (w,g)=(0,6) -> 1. If any cube is painted via (w,g)=(5,1) or (1,5), any other cube painted (1,5) or (5,1) will be alike. So this yields 2 more possibilities for uniques cubes. The other choices are
(w,g)=(4,2)
(w,g)=(3,3)
(w,g)=(2,4)
Besides these three, you have the 4 possibilities for uniqueness that I described above. For the (4,2) AND the (2,4) case, you have two possibilities EACH. One is if the two green faces are touching, and one is if the green faces are on opposite sides of the cube. Same for white. Therefore you have four more.
Then you have 8 possibilities plus the possibilities for (3,3). If you have two whites opposite one another and one white touching each of those, it can be rotated into any other of the three similar formations. That's one. See if you can find the rest for (3,3).

Answer 4

cube has 6 faces , you can color them with 2 colors in 2 ^ 6 = 64 ways.

this is overcounting because by rotation the cubes can have the same color scheme. yo have to divide by the number of rotations.

Answer 5

1. allele. An alternetive form of a gene for a single trait. Example, color of the eyes: blue(BB), green(bb). 2. Segregation 3. First progeny, first offspring generation 4. Assortment