Cube problems

[assignus]

Originally Posted by j0

yeah he did make a mistake, and couldn't the question be interpreted to mean just cover all the surfaces of the cube and hence we'd need the TSA?
6x5^2= 150

right(150)....6 faces x (5x5) each face......cubes at the corners are not required...so 218 is wrong.....

[GauravShah]

Originally Posted by Eccentric

I think Gaurav made a midstake here.
Size of larger cube = 125^1/3 = 5

The size of zube to completely engulf the cube of size_5 = 7

Think of it like what size of square is required to cover a squzre of size 5 from all sides.
6 will not do.. we need square of size 7.

no of small cubes = 7^3 = 343
more needed = 218.

Originally Posted by j0

yeah he did make a mistake, and couldn't the question be interpreted to mean just cover all the surfaces of the cube and hence we'd need the TSA?
6x5^2= 150

yeah my mistake . you are correct, it shud have been 7

[j0]

assignus my friend...you have no idea how long i've been waiting for that validation.
Chalo there is hope for me in quant after all.

[GauravShah]

Originally Posted by assignus

right(150)....6 faces x (5x5) each face......cubes at the corners are not required...so 218 is wrong.....

no it has to be 218, have solved these kind of problems from the TIME booklet, the after covering, it should form a cube again.

But still we can wait for sarab to post the correct answer i guess.

[GauravShah]

Originally Posted by GauravShah

First find factors of 24
24 = 2 x 2 x 2 x 3

Now write the number (24) in terms of 3 factors of least possible value.

So its 24 = 2 x 3 x 4.

Cuts required = (a-1) x (b-1) x (c-1) = 1 x 2 x 3 = 6

Originally Posted by made_for_iims

Shouldn't it be 24 = 2*2*2*3

so total number of cuts needed 1+1+1+2 =5 cuts

Originally Posted by FreakazoiD

Can you explain this formula ?

The way I would solve this is : (dont have a formula, just intuitive...)

The max no. of pieces I can get from one cut is 2. For each additional cut, I can make pieces in multiples of 2 (if I cut elsewhere, the no. of pieces decreases). SO I can get 4 pices from 2 cuts, 8 from 3 and 16 from 4. 5 cuts will give me a maximum of 32 pieces. But we need just 24 here, so I would say the answer is 5.

cheers,

the freak

The number needs to be in terms of 3 factors, coz the factors represents the 3 axis. So 5 will be wrong.

freak, yeah by 3 cuts on 3 axis, we can have 8 smaller pieces, but with 4 cuts we cannot have 16 smaller pieces.

Actually there is a reverse kind of a problem too, like how many smaller pieces can be made using 4 cuts.

Here you divide the number into three parts of close values.

4 can only be divided as 1,1,2.

So the parts in each axis is 2 , 2 , 3. Total smaller pieces = 2 x 2 x 3 = 12.

I know that maybe its still not clear, still am quite sure about this and please post your doubts if any

HTH

Gaurav.

[made_for_iims]

Originally Posted by GauravShah

The number needs to be in terms of 3 factors, coz the factors represents the 3 axis. So 5 will be wrong.

freak, yeah by 3 cuts on 3 axis, we can have 8 smaller pieces, but with 4 cuts we cannot have 16 smaller pieces.

Actually there is a reverse kind of a problem too, like how many smaller pieces can be made using 4 cuts.

Here you divide the number into three parts of close values.

4 can only be divided as 1,1,2.

So the parts in each axis is 2 , 2 , 3. Total smaller pieces = 2 x 2 x 3 = 12.

I know that maybe its still not clear, still am quite sure about this and please post your doubts if any

HTH

Gaurav.

Oops....I missed such a simple thing.... You are right.....It has to be multiple of 3...

Thx

[sarab]

Originally Posted by GauravShah

The number needs to be in terms of 3 factors, coz the factors represents the 3 axis. So 5 will be wrong.

freak, yeah by 3 cuts on 3 axis, we can have 8 smaller pieces, but with 4 cuts we cannot have 16 smaller pieces.

Actually there is a reverse kind of a problem too, like how many smaller pieces can be made using 4 cuts.

Here you divide the number into three parts of close values.

4 can only be divided as 1,1,2.

So the parts in each axis is 2 , 2 , 3. Total smaller pieces = 2 x 2 x 3 = 12.

I know that maybe its still not clear, still am quite sure about this and please post your doubts if any

HTH

Gaurav.

Gaurav
i didnt get this logic.

suppose i need to cut the cube by 10 cuts ....
i can split it 2 ,3,5 therefore 3*4*6= 72 identical cubes ..but answer is 44
for 3 cuts and 4 cuts it comes correct as 8 and 12.


try for 13 too ...i didnt follow as u rightly said

[sarab]

Originally Posted by GauravShah

Quote:
Originally Posted by sarab
3)125 small but identical cubes are cut to form a large cube.This large cube is now painted on all six faces.
How many of the smaller cubes have no faces painted at all / have exactly one face painted?

Using Formula

No faces painted = (n-2) x (n-2) x (n-2)

So since cubes is of 5 x 5 x 5. Number of cubes with no face painted = 3 x 3 x 3 = 27

1 face painted = 6 x (n-2) x (n-2)

So its = 6 x 3 x 3 = 54

Gaurav
how do u genralise the above formul
no faces u said subtract by 2 okie it works
but for 1 face painted ? u have taken 6 *n-2 *n2 ?????

how u derived the same and how about 2 faces 2 faces and so on ???
do explain the answer and formula how got that?

[look_beyond_CAT]

Originally Posted by sarab

1) 125 small but identical cubes have been put together to form a large cube.how many such small cubes would be required to cover this large cube compeltely?

Originally Posted by GauravShah

no it has to be 218, have solved these kind of problems from the TIME booklet, the after covering, it should form a cube again.

But still we can wait for sarab to post the correct answer i guess.

Step 1)



cubes added = 7x7=49






Step 2)



cubes added = 5x7=35





Step 3)



cubes added = 5x7=35






Step 4)



cubes added = 7x7=49






cubes required to cover the "top" and "bottom" = 5x5 + 5x5 = 50

Total cubes required = 49+35+35+49+50= 218


Niraj

[j0]

1) 125 small but identical cubes have been put together to form a large cube.how many such small cubes would be required to cover this large cube compeltely?

sarab post the answer to this one.. we don't seem to be agreeing on the interpretation.