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# what is the maximum possible number of identical pieces a cube can be cut into by 12 cuts?

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## [Solved] What is the maximum number of pieces into which a cube can b

Given:  A cube that has been applied 13 cuts.  Concept: By cutting the cube for the first time, it will be divided into 2 parts.  By cutting Home Quantitative Aptitude Mensuration Solid Figures Cube

## What is the maximum number of pieces into which a cube can be cut by 13 cuts?

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## Detailed Solution

Given:

A cube that has been applied 13 cuts.

Concept:

By cutting the cube for the first time, it will be divided into 2 parts.

By cutting the cube along the perpendicular, it will be divided into 4 parts.

Again, by cutting the cube along the perpendicular, it will be divided into 8 parts.

⇒ With 3 cuts, there will be a total of 8 cubes.

⇒ It can be concluded that 'n' cuts made along one plane will have 'n + 1' pieces.

Calculation:

To obtain equal pieces, cuts must be made parallel to 3 planes.

Let's assume, a, b, and c cut made along three planes such that there will be (a + 1)(b + 1)(c + 1) = m pieces & a + b + c = 13.

⇒ Several combinations can be made but 'm' will be maximum in (4, 4, 5) cuts.

∴ The required number of pieces = m = (4 + 1)(4 + 1)(5 + 1) ⇒ 5 × 5 × 6 ⇒ 150

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## What is the maximum number of pieces into which a cube can be cut by 12 cuts?

Answer (1 of 3): I don’t know the answer but it is at least 125. This the number of pieces you get if you make 4 cuts parallel to each of the 3 pairs of parallel faces. The relevant mathematics is called Polya counting after the mathematician George Polya. I have tried to find a suitable link wi... What is the maximum number of pieces into which a cube can be cut by 12 cuts?

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What is the maximum number of identical pieces a cube can be cut into by 4 cuts?

Any Japanese chef can give you a far better answer to this than your typical mathematician will. A mathematician might tell you 12 or 16 depending upon whether they rearrange the pieces before cutting. However a Japanese chef will tell you “thousands” and that is meant literally. Not only can it be done, it is indeed regularly done by these chefs. The secret is called the Katsuramuki technique. Quite simply, the first cut is a spiral, which is normally done by hand with a sharp knife on a log-shaped vegetable such as Daikon, resulting in a long sheet, but could work with a cube by gradually ro

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What is the maximum number of cuts by which a cube can be cut into 27 pieces?

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Bruno Curfs

M.Sc. in Mathematics & Information Technology, University of Utrecht (Graduated 1993)Author has 1.1K answers and 1.7M answer views4y

Greatest number of parts in which n planes can divide the space

Here, the cake number C(n) is defined for n the number of cuts, and the question asks to calculate C(12).

The first insight is that the form to be cut can be any convex form. Consider all points through which 3 planes go. These points are bounded. If you multiply such a maximal division by a factor <1, the configuration of these intersection points can be made to fit any finite region. If it’s a ball, you can then see that continuously expanding the ball into a cube will not change the number of pieces. This can be generalized to al

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I don’t know the answer but it is at least 125. This the number of pieces you get if you make 4 cuts parallel to each of the 3 pairs of parallel faces.

The relevant mathematics is called Polya counting after the mathematician George Polya. I have tried to find a suitable link without success. Here is a link about Polya himself:

George Pólya - Wikipedia

Edit: I was assuming that the pieces remain in their original positions. If restacking is allowed then the answer is 2^12 = 4096.

Doug Dillon

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What is the maximum number of smaller identical pieces a cube can be cut into by making 17 cuts?

Let’s make cuts parallel to the face planes of the cube. If we make a cuts parallel to 2 opposite faces,

a+1 a+1

identical pieces might reveal themselves.

Same with the other two pairs of opposite faces for a total of

(a+1)(b+1)(c+1) (a+1)(b+1)(c+1) pieces. So we maximize (a+1)(b+1)(c+1) (a+1)(b+1)(c+1) subject to a+b+c=17 a+b+c=17

. Unfortunately, I see no way to continue apart from a little brute force. But I hope the numbers

a,b, a,b, and c c

will be was close together as possible. Perhaps,

a=5,b=6 a=5,b=6 and c=6 c=6 , making 294 294 pieces. Edward Sherry

Worked at Expert Research AssociatesAuthor has 4.8K answers and 3M answer views4y

The answer depends on whether you are allowed to restack the pieces between cuts. If you are, you can get more pieces than if you’re not.

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Midhilesh Momidi

Data Scientist at EY (Ernst & Young) (2021–present)3y

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If five cuts are made on a cube, what is the minimum number of pieces obtained?

Take a Cube and 1 cut gives 2 pieces and if we cut perpendicularly we get 4 pieces or a parallel cut gives one extra piece so total 3

So to get minimum number of pieces we need to cut the cube in parallel.

1 cut 2 pieces 2 cuts 3 pieces

…n cuts gives n+1 pieces

So 5 parallel cuts gives 6 pieces minimum

Alexander L

Studied at Stormtrooper School of Shooting at ThingsAuthor has 13.8K answers and 33.4M answer views4y

Related

How can you cut a pizza in 3 pieces with only 2 cuts?

Here’s one way: However, someone will end up with a significantly larger piece.

स्रोत : www.quora.com

## What is the maximum number of identical pieces a cube can be cut into by 13 cuts?

What is the maximum number of identical pieces a cube can be cut into by 13 cuts? Home Engineering

What is the maximum number of identical pieces a cube can be cut into by 13 cuts?

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What is the maximum number of identical pieces a cube can be cut into by 13 cuts?

First cut will divide the cube in 2 parts. The second cut along perpendicular direction will double the number of parts to 4, now the 3rd cut will also be in perpendicular direction which will double the 4 parts to 8. So totally 8 cubes can be formed with 3 cuts. All the 3 direction should be perpendicular to each other.

Note that 1 cut = 2 parts of cube, 2 cut = 3 parts and so on.

x cuts made along one plane results in x + 1 pieces.

Logic behind this is, divide the given number of cuts in 3 equal parts and put that many cuts on each perpendicular direction.

For obtaining identical pieces, cuts must be made parallel to 3 planes of the cube.

Let we made x, y, z cuts along all three planes such that (x+1)(y+1)(z+1) = t is maximum & x + y + z = 13.

Different combinations can be possible but t will be maximum in (4, 4, 5) cuts.

So maximum pieces = (4 + 1) * (4 + 1) * (5 + 1) = 5 * 5 * 6 = 150.

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