How to solve cube problems, like a big cube is divided into 64 smaller cubes. Some sides are painted in blue, red or green. Can you plz. guide me how to approach these types of problems?

The given question is not fully correct .

I will give u another eg ...

If a cube is painted red and  cut into 64 pieces .

Approach this question as ,,

64 pieces = 4 *4* 4   so take  n=4

just use this formula

1. no sided painted  =(n-2)^3

2. 1  sided painted =6 * (n-2)^2

3. 2  sided painted = 12 *(n-2 )

4.  3 sided painted = always 8 (a cube has 8 corners)

reffer R.S.Agarwal's 'verbal non-verbal reasoning' book...concept cubes

It is very easy to solve cube problems. there is a simple solution to solve cube problems if we use formulae.

Before solving the color cube problem first we have to solve the no of 1 side,2 side, 3 side and central cubes in a huge cube.

Formulas:
If we cut the cube into x number of halves, the total number of small cubes is (no. of halves) power 3.

the number of central cubes is -----------------" (number of Middle columns) power 3"
the number of 1 sides is -------------------------" Number of faces * central cubes"
the number of 2 sides is -------------------------"Number of two sides in one face* 3"
the number of 3 sides is -------------------------"Number of Corners" i.e.. 8 .

For eg
One cube is divided into 5 halves then
the number of central cubes == ( number of Middle columns) power 3== 9 power 3 ==27
the 1 side cubes == Number of faces * central cubes == 6 * 9 ==54
the 2 side cubes == Number of two sides in one face* 3 == 3 * 12 ==36
the 3 side cubes == Number of Corners == 8
------------------
Total number of cubes ==125
---------------------

After calculating this based on the color information we have to decide the answer for the questions.

for eg

If a cube is colores red on one face, green on the opposite face,yellow on another face and blue on a face adjacent to the yellow face. the other two faces left uncolored. it is cut into 125 smaller cubes of equal size.

Q: How many cubes are uncolored on all faces?
A: Here two faces are uncolored
So the total number of 1 side cubes on two sides is == Central cubes+ 1 side for two faces+ uncolored common cubes for those two faces.
i.e.. 27+(2*9)+3 === 48

HI can you please explain what is meant by middle column. how you are calculating it

There is no particular formula used to solve this type of question but better understanding of the question helps to to respond quickly

ANSWER:suppose the initially the length of the side of the cube is x.After cutting the cubes into 64 smaller sub cubes the sides of each cubes will be x/4(since 64=4*4*4. in case of 125 smaller sub cubes length of each side will be x/5.......)
now you can solve the question easily according to the question that which face is painted in which color

In above example the value of n should be 3 but not 4. Because when you give 4 cuts in same direction the cube will be divided into 5 parts. So n(the number of cuts) will be always one less than the total number of parts on each side.

4x4x4=64 so 4 parts on each side.
3 cuts will make 4 parts.
3x3x3 so 3 cuts on each side of cube.

Instead of analyzing the properties of cube its very easy 2 remember the formulas...
we can get answer very fast too.......
thanx

write 1 to 5 numbers on a paper(1,2,3,4,5). Now strike the number 1 and 5. then count the numbers u r having at d middle. there are 3 numbers. In the same way take a cube and eliminate left side corner boxes and right side corner boxes. Then count any 1 line boxes horizontally.

I solved the cube in another manner and was unable to get ur answer? How is it so?

Mr Sooraj... Second formula should be 6*(n-2)^2

Hi,
The mean of middle column is the column which are not in boundary. thats why we here use (n-2)