**Sooraj Prabhakaran**
Answered On : Jan 1st, 2007

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)

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

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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

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

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**vikrant dwivedi**
Answered On : Aug 9th, 2011

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

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**Mandar**
Answered On : Oct 17th, 2011

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.

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**sathish**
Answered On : Jan 7th, 2012

Instead of analyzing the properties of cube its very easy 2 remember the formulas...

we can get answer very fast too.......

thanx

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**sugins**
Answered On : Mar 29th, 2012

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.

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**Sanil**
Answered On : Jun 11th, 2012

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

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**Sandeep**
Answered On : Sep 4th, 2012

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

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**Akansha**
Answered On : Dec 11th, 2012

Hi,

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

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