what is the maximum possible number of identical pieces a cube can be cut into by 11 cuts?
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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?
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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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What is the maximum number of smaller identical pieces a cube can be cut into by making 17 cuts?
Answer (1 of 4): If you allow the parts you already cut to be regrouped, then the maximum equals 2^17 = 131,072 pieces. Step 1. You start with the cube and cut it in half. You get 2 identical cuboid blocks. Step n. You start with 2^(n-1) identical cuboid blocks. Stack them, keeping the sides fl...
What is the maximum number of smaller identical pieces a cube can be cut into by making 17 cuts?
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Sort Doug Dillon
I answered the question below.Author has 9.8K answers and 8M answer views4y
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. Related questions
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Henry Ha
Lives in Brisbane, Queensland, AustraliaAuthor has 137 answers and 78.9K answer views2y
17 cuts = 18 pieces …
otherwise if its 3 dimension…. *brain explodes*
more cuts = more cubes
5+6+6 = 17 , 5*6*6 = 180 > 4*6*7 = 168
so 180 ?
1 cut = 2 piece, 2 cut = 3 piece,3 cut = 4 piece
so 5 cut = 6 piece, and 6 cut = 7 piece
so 5*6*6 becomes 6 * 7 * 7 = 294 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 viewsUpdated 2y
If you allow the parts you already cut to be regrouped, then the maximum equals 2^17 = 131,072 pieces.
Step 1. You start with the cube and cut it in half. You get 2 identical cuboid blocks.
Step n. You start with 2^(n-1) identical cuboid blocks. Stack them, keeping the sides flush. Then, cut the stack in half top-down. You get 2^n identical cuboid pieces.
Repeat step n for n = 2 to 17.
Note. Rather than stack them, there are other ways of grouping them, but it was the easiest way to describe. For instance, you can stack them, laying them on their largest surface or the smallest. In the former case
David Rutter
B.S. Discrete Mathematics, Georgia TechAuthor has 8.5K answers and 8.3M answer views3y
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What is the max number of identical pieces a cube can be into by 7 cuts?
As long as you can restack the pieces after each cut, you can double the number of pieces with each cut, giving you a total of 128 identical pieces.
If you can't restack them, i.e. all the cuts happen instantly while the cube is suspended in the air, you can get at least 36 identical pieces.
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
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Neshar Ahmed
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Let’s build cuts parallel to the face planes of the cube. If we have a tendency to build a cuts parallel to a pair of opposite faces, a+1 identical items may reveal themselves.
Same with the opposite 2 pairs of opposite faces for a complete of (a+1)(b+1)(c+1) items.
So we have a tendency to maximize (a+1)(b+1)(c+1) subject to a+b+c=17. sadly, I see no thanks to continue aside from a touch brute force. however I hope the numbers a,b,and c are going to be was approximate as potential. Perhaps, a=5,b=6 and c=6, creating 294 items.
Aaron Jantzen
Loophole developer and exploiterAuthor has 3.4K answers and 14M answer views4y
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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
[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
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What is the maximum number of pieces into which a cube can be cut by 13 cuts?
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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 ⇒ 150Download Solution PDF
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