# what is the least possible number of cuts required to cut a cube into 37 identical pieces?

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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 minimum no. of cuts required to cut a cube int 216 indentical pieces of cube ?

What is the minimum no. of cuts required to cut a cube int 216 indentical pieces of cube ?

Home > English > Class 12 > Maths > Chapter > Question Paper 2017 >

What is the minimum no. of cut...

What is the minimum no. of cuts required to cut a cube int 216 indentical pieces of cube ?

( 00 : 00 ) Text Solution Open Answer in App A 36 B 15 C 18 D 12 Answer

The correct Answer is A

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## What is the least number of cuts required to cut a cube into 24 identical cuboids if you are not allowed to rearrange the cut pieces?

Answer (1 of 4): All cuts must be parallel to one side and at right angles to two others; otherwise you don’t get cuboids. (This argument needs work). The easiest case is slicing down through the top to get 6x4 vertical cuboids. This gives you 24 identical elongated cuboids with (6–1) + (4–1) or...

What is the least number of cuts required to cut a cube into 24 identical cuboids if you are not allowed to rearrange the cut pieces?

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Sort Joe Schlessinger

Works at RetirementAuthor has 92 answers and 35.7K answer views4y

All cuts must be parallel to one side and at right angles to two others; otherwise you don’t get cuboids. (This argument needs work).

The easiest case is slicing down through the top to get 6x4 vertical cuboids. This gives you 24 identical elongated cuboids with (6–1) + (4–1) or 8 cuts.

Systematically, how many ways can you factor 24 into 1, 2, or 3 factors? (3 for 3 dimensions)

24 x 1: slice the top in one direction 24 times. 23 cuts

12 x 2. Slice the top into 12 slices and the cut the middle once horizontally. 11 + 1 = 12 cuts

6 x 4: slice the top in 2 directions into 6 and 4 slices. 5+3 = 8 cuts

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How can I find out the number of cuts required to divide a cube into 120 smaller cubes?

Cliff Williams

Author has 88 answers and 15.4K answer views2y

If each cuboid is rectangular (but not a perfect square) then I reckon on 5 straight cuts.

3 equal spaced cuts on one face (gives 4 identical pieces)

Then 2 equal spaced cuts on the 2nd face (gives 6 x 4 = 24 pieces).

…unless it is a trick question and I have been caught!

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Dee Stoddard

3x AS in Computer Networking & Mathematics, Heald College (Graduated 2004)Author has 186 answers and 123.2K answer views2y

Cut each of the 3 dimensions into = 3rd by 2 cuts each.

2*3=6

You will have 27 perfect cubes

If you want 24 exactly, factor out 24 to 2,2,2,3

Splitting these 4 into 3 could be

2,3,4 or 2,2,6 or 1,3,8 or 1,4,6 or 1,2,12 or 1,1,24

2,3,4 adds up to the smallest # and also requires 6 cuts. Each side # of cuts is 1,2,3. these are not perfect cubes but would be identical to each other.

Bryan Ferraro 4y

By Popova’s Theorem, the fewest number of cuts to cut a cuboid into 24 identical cuboids is 5. If, however, you use a stiff knife, use Serpinski and get 6. Sorry.

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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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.

So, what if you make a curved cut, like this:

This way, the pizza is distributed a lot more evenly. Still not perfect, but it’s close enough. This is perhaps the best way, as it ensures that everyone has approximately equal amount of crust and non-crust.

You could also do this (a.k.a. the “Scissor” cut) :

But then two people would get significantly more crust.

Or this (a.k.a. the “Fuck it.” cut):

And of course, there’s this (a.k.a. the “Greedy sonofabitch” cut):

David Rutter

B.S. Discrete Mathematics, Georgia TechAuthor has 8.5K answers and 8.3M answer views3y

Guys, does anyone know the answer?