# what is the least possible number of cuts required to cut a cube into 150 identical pieces?

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## Minimum possible number of cuts required to cut a cube into 150 pieces

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Monisha Sep 25, 2017 Related

Minimum possible number of cuts required to cut a cube into 150 pieces

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## What is the least possible number of cuts required to cut a cube into 150 identical pieces

According to the question We have to find the least possible number of cuts so the total count of pieces got withxy and z axis are X1xY1xZ141x41x51 Thus the total no of cuts are5x5x6150 Least no of possible cuts are 44513 Hence this is the final answer

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Cubes and Dices>Practice Exercises>Q 20

EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT Earn 100

What is the least possible number of cuts required to cut a cube into

150 identical pieces? 50%

students answered this correctly

## Important Questions on Cubes and Dices

EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Non-Verbal Reasoning>Exercise>Q 1

Directions for Questions: There is a relation between figures A and B. Choose a similar relationship between C and D by choosing a suitable figure D from the answer set.

Problem Figures Answer figure EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Non-Verbal Reasoning>Exercise>Q 4

Directions for Questions: There is a relationship between A and B of the problem figures. Establish a similar relationship between C and D by selecting a suitable figure from the Answer Set.

Problem Figures

Answer Figures

EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Non-Verbal Reasoning>Exercise>Q 5

Directions for Questions: There is a relationship between A and B of the problem figures. Establish a similar relationship between C and D by selecting a suitable figure from the Answer Set.

Problem Figures

Answer Figures

## Important Points to Remember on Cubes and Dices

**Cubes and Dice**

**1.**On a die, the sum of the number on the opposite faces will always be equal to ‘

7 ’. The number 1 will be opposite to 6, 2 is opposite to 5 and 3 is opposite to 4 .

**2.**If one of the numbers is common in both the dice when two dice have the same surface, then the remaining surfaces of both the dice are opposite to each other.

**3.**If only one element is common on both the dice but at a different position, then rotate the dice in a clockwise direction using the common side to get the opposite surface.

**4.**Here, the clockwise pattern is

265 and 241 . Hence, 6 is opposite to 4 and 5 is opposite to 1 . Thus, 4 is opposite to 2 .

**5.**There are three different types of open die:

**6.**Here,

1 is opposite to 5. 2 is opposite to 4. 3 is opposite to 6 .

**7.**Here,

1 is opposite to 6. 2 is opposite to 4. 3 is opposite to 5 .

**8.**Here,

1 is opposite to 3. 2 is opposite to 5. 6 is opposite to 4 .

**Points to remember about cubes:**

i. A cube has 6 faces, 12 edges and 8 vertices.

ii. For n cuts mutually parallel to the base (or any other face), we get

n+1 solid pieces.

iii. On painting the outer surface of a cube with the same colour:

(a) Number of cubes with

3 faces painted = 8

(b) Number of cubes with exactly 2 faces painted

=(n-2)× (number of edges)

(c) Number of cubes with exactly 1 face painted

=(n-2)2×6

(d) Number of cubes with 0 faces painted black

=(n-2)3=8

## Questions featured in Previous Year Papers on Cubes and Dices

EASY PREVIOUS YEAR

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Cubes and Dices>Practice Exercises>Q 12

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing

## What is the minimum number of cuts required to cut a cube into 50 identical pieces?

Answer (1 of 4): * The product of three numbers with 50 with minimum sum of the three numbers is the answer. * So a x b x c = 50 The value of a,b,c with minimum (a+b+c) value is 5 ,5 ,2. * Therefore if we have 5- parts along the length 5- parts along the breadth and 2-parts along the height wi...

What is the minimum number of cuts required to cut a cube into 50 identical pieces?

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Sort Taruna Agrawal

Btech from The LNM Institute of Information Technology (LNMIIT) (Graduated 2021)2y

Factorise 50 in form of a*b*c where a,b,c are as close as possible then subtract 1 from each multiplier and add them.

a,b,c are the no of pieces when cut from one of dimensions of 3D respectively.

a-1, b-1,c-1 are the cuts to get those pieces in each dimension

Possible factors are-

1*5*10 ( 0+4+9=13 ) 2*5*5 ( 1+4+4=9 )

Later one is having least sum so 9 cuts required to get 50 pieces.

Related questions

How many cuts are needed to cut a cube to 60 pieces?

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

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?

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

Can two identical cubes be cut into pieces and rearranged to form a single, larger cube?

John K Williamsson

Accredited (MS Educ) nerd who loves talking about mathAuthor has 6.4K answers and 16.7M answer views2y

I don’t know if this is the best answer, but here’s how I got 9 as a potential answer:

What is a factorization of 50 = a × b × c that has the smallest possible sum?

* 1 × 5 × 10 → 1+5+10 = 16

* 1 × 2 × 25 → 1+2+25 = 28

* 2 × 5 × 5 → 2+5+5 = 12 ← we have a winner

What does 50 = 2 × 5 × 5 and 1+4+4=9 tell us? (I subtracted 1 from each factor)

* We want two identical layers, which requires one cut

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Vasudevan A.N.S.

Former Retired Professor of Chemistry. (1977–2014)Author has 7.8K answers and 9.1M answer views1y

The product of three numbers with 50 with minimum sum of the three numbers is the answer.

So a x b x c = 50 The value of a,b,c with minimum (a+b+c) value is 5 ,5 ,2.

Therefore if we have 5- parts along the length 5- parts along the breadth and 2-parts along the height will give 50 - identical pieces.

So actual number of required cuts along the length, breadth and height wise will be (5–1),(5–1) and (2–1) = 4,4 and 1 cuts.

So a minimum of 9-cuts along the length, breadth and height wise will give the result.

Tom Fyfield

Studied Pure Elemental MathematicsAuthor has 1.2K answers and 417.1K answer viewsUpdated 1y

What is the minimum number of cuts required to cut a cube into 50 identical pieces?

13 is my answer.

9 virtual cuts will give us 10 identical slices

and 4 horizontal cuts gives us 5 the other way .

5 times 10 equals 50

And 9 plus 4 equals 13

Edit… It appears I am mistaken here 4 x 4 x 1 gives 9 cuts.

Nrusingha Charan Behera

B.Tech(Agril. Engg ) in Mathematics & Physics, Orrisa University of Agriculture & Technology, Bhubaneswar (Graduated 1993)Author has 5.5K answers and 4M answer views3y

Related

What is the minimum number of cuts required to cut a cube into 420 pieces?

As 420=10×7×6. So the number of cuts needed on the very sides is

(10–1)+(7–1)+(6–1)=20.Ans..

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Joe Schlessinger

Works at RetirementAuthor has 92 answers and 35.7K answer views4y

Related

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?

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

Doug Dillon

I answered the question below.Author has 9.8K answers and 8M answer views4y

Related

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,

Guys, does anyone know the answer?