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    what is the least possible number of identical pieces a cube can be cut by 17 cuts?

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    Find the least number of cuts required which can cut a cube into 60 identical pieces?

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    Question

    Find the least number of cuts required which can cut a cube into 60 identical pieces?

    A

    9

    B

    12

    C

    15

    D

    5

    Medium Open in App

    Updated on : 2022-09-05

    Solution Verified by Toppr

    Correct option is A)

    We need to cut a ute to 60 identical pieces

    If we cut oru it become 2 identical pieces.

    If we cut twice on same face it becomes 3 identical pieces.

    If we cute once on one face and another on other face it becomes 4 identical pieces.

    ∴ general formula ⇒ number of identical pieces=(l+1)(m+1)(n+1)

    (n,m,l)= no. of cut on each face

    Given:- (l+1)(m+1)(n+1)=60

    (l+1)(m+1)(n+1)=3×4×5

    ⇒(l+1)=3,m+1=4,n+1=5

    ⇒l=2,m=3,n=4

    ∴ total no. of cuts =l+m+n=3+4+2

    =9

    ∴ minimum 9 cuts have to be made to get 60 identical pieces.

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    What is the maximum number of identical pieces that a cube can be cut into by 15 cuts?

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    What is the maximum number of identical pieces that a cube can be cut into by 15 cuts?

    What is the maximum number of identical pieces that a cube can be cut into by 15 cuts? Question:

    What is the maximum number of identical pieces that a cube can be cut into by 15 cuts?

    Cuboid - Cube:

    A cuboid is a three dimensional solid that represents a rectangular box that has straight walls arranged perpendicularly. A cube is a cuboid that has all the walls of the same dimension. A geometric shape can be divided into

    N + 1 N+1 parts with N N cuts.

    Answer and Explanation:

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    Let us assume that the cube is cut in two cuboid with a single cut along a plane parallel to x-y axis. To create identical shapes same number of...

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    Learn more about this topic:

    How to Calculate the Volume of a Cube: Formula & Practice

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    Chapter 18 / Lesson 12

    635K

    Learn how to find the volume of a cube. View the formula for calculating the volume of a cube. See examples of how to calculate the volume of a cube using its side length, surface area, or diagonals.

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    स्रोत : homework.study.com

    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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    If 10 cuts are made on a cube, what will be the maximum number of identical pieces obtained?

    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

    Related

    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

    Related

    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

    Student at Studying3y

    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

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