What is the minimum number of cuts required to cut a cube into 294 pieces

What is the minimum number of cuts required to cut a cube into 294 pieces. Click here:point_up_2:to get an answer to your question :writing_hand:45 find the least number of cuts requirednto cut a cube into 84 identical piecesnassuming Jan 19, 2023 · Puzzle 31 | (Minimum cut Puzzle) Puzzle: You have got someone working for you for five days and a gold bar to pay him. Cannot be determined A diamond expert cuts a huge cubical diamond into 960 identical diamond pieces in minimum number of 'n' cuts. Dec 13, 2017 · A cube is painted and cut into 64 smaller but identical pieces by making the minimum possible number of cuts. Furthermore, after Jan 20, 2021 · 2nd cut --> 4 pieces. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set. Direction: A cube is painted and then divided cut into 336 smaller but identical pieces by making the minimum number of cuts possible. Jan 9, 2024 · To cut a cube into 32 identical pieces, a minimum of 7 cuts is required. In other words, the cube should be divided into Apr 15, 2009 · A cube is to be cut into 27 smaller cubes (just like a Rubik's Cube). Sep 24, 2007. 2nd day: Takes back 1 unit cut from employee given on the first day and gives 2 unit cut. How many cuts are required to cut a cube into 512 pieces? 4. 3rd Day: Gives 1 unit and then the employer is left with 4 unit rod lengths. 125 b. When 1 of the cornal is sliced, we get an image or a shape, as shown here, as this is not drawn to scale anyway. All the 3 direction should be perpendicular to each other. Suppose the cube is oriented with one corner at the origin and the opposite corner at (6,6,6). Minimum no of cuts required is 3+3+5=11. What is the minimum number of cuts required to cut a cube? i ح ث A. of cuts = (3-1)+(5-1)+(8-1) = 13. 4. What is the minimum number of cuts required to cut a cube? There are 6 minimum cuts which is required. No Painted Face = ( 9 - 2)³ = 7³ = 343. Was this answer helpful? Click here:point_up_2:to get an answer to your question :writing_hand:find the least number of cuts required which can cut a cube into 60 identical Aug 13, 2020 · How many cuts are required to cut a cube into 45 pieces? Minimum number of cuts required to cut a cube into 45 identical pieces 2 See answers efimia efimia Answer: 11 cuts. This drawing is only a rough one. Let us write 120 as the product of 3 numbers = 1*1*120, 1*2*60, 1*3*40,. Apr 14, 2023 · 1. Oct 31, 2021 · By cutting the cube along the perpendicular, it will be divided into 4 parts. By making three cuts along one dimension and two cuts along the other two dimensions, you can achieve 32 equal parts due to the compounding effect of the cuts in three-dimensional space. There is a rough drawing. The 3rd cut can make 3 + 3 = 6 pieces and so on. 140 c. 3. Q5: How many minimum cuts you have made? (a)15 (b)18 (c)21 (d)9. And to divide into five parts, each edge will have to be cut 5-1 = 4 times Hence, the number of times the cube has to be cut = 4×3 = 12. The correct answer is 6. Then take one piece and stack it on top of the other, and make two cuts at x=1 and x=2. Thus, the minimum number of cuts which are required to cut the cube into 40 identical Nov 5, 2019 · A cube is painted and cut into 729 smaller and identical cubes by making the minimum possible number of cuts. Solution. What is the minimum possible number of cuts required to cut a cube into 180 pieces? 5. Viewed 1k times. We know that whenever a three dimension symmetrical figure is cut along any axis, it always gives one plus identical figures. NTSE. In the case of a cube, the maximum number of identical pieces it can be cut into by 16 cuts is 162. The cuts divide the cube into 27 one-inch cubes. 5+3 = 8 cuts. How many smaller cubes have exactly two painted faces? What is the maximum number of identical pieces a cube can cut into by 3 cuts? Option 1) 9 Option 2) 8 Option 3) 4 Option 4) 6 Option 5) 7 Apr 26, 2024 · The maximum number of identical pieces a cube can be cut into by 3 cuts is 8. Hence a = b = c = 8 is the minimum number of cuts. It has a few sides. What is the maximum number of identical pieces a cube can be cut into by 13 cuts. May 19, 2019 · cube has 6 faces . 120 b. 4th cut --> 16 pieces. The minimum number of such cuts required is Apr 28, 2022 · If no cut intersects any previous cuts, then you can just slice it into 14 pieces. With each subsequent cut, while considering maximum pieces, you can add as many pieces as the cut number. Sep 13, 2023 · Number of pieces required = 120. So totally 8 cubes can be formed with 3 cuts. VIDEO ANSWER: We have a cube. 5-6): A cube is divided into 343 identical cubelets. What are the fewest number of cuts to the bar of gold that will allow you to pay him 1/5th each day? Answer: 2 cuts. . . The answer to the question will be that 1 of A cuboidal block of 6 c m × 9 c m × 1 2 c m is cut up into an exact number of equal cubes. Modified 5 years, 7 months ago. Directions for questions 6 to 9: A cube is painted and cut into 343 smaller but identical pieces by making the minimum possible number of cuts. Then we cut another 5 cuts parallel to the first surface. 18 A. The third cut cannot cut all the 4 pieces, it can cut only 3. You must give them a piece of gold at the end of every day. You'd have to have 5 equally distant points and this isn't achievable in a cube if you leave the center of symmetry, with a We could use five cuts, or we could cut twice along one axis and once along the axis perpendicular. Calculation: To obtain equal pieces, cuts must 343 pieces? 6. It means you need exactly 6 cuts to make the central cube. 0. If we cut twice on the same face it turns into 3 identical pieces. The least possible number of cubes will be The least possible number of cubes will be Easy Oct 7, 2016 · What is the least number of cuts required to cut the cube into 24 identical pieces? (A) 2 (B) 4 (C) 6 (D) 8 (#M40014378) MBA question number systems, progressions Keep an EYE What is the least number of cuts required to cut a cube into 84 identical pieces, assuming all cuts are made parallel to the faces of the cube? 1) 11 2) 12 3) 13 4) 10 Asked In MBA (11 years ago) Unsolved Read Solution (1) Jul 14, 2023 · Answer: 6 cuts is required. Another way to imagine this is a circle and a pentagon. 0. 200 Nov 3, 2021 · What's the maximum number of pieces that can be obtained with 17 cuts without putting the pieces one above another? Here, we can split 17 as 5, 6 and 6 which is the most equally distributed case. Jan 15, 2024 · To find the maximum number of identical pieces a cube can be cut into by 15 cuts, optimal distribution of cuts along the cube's three dimensions is considered. Jan 20, 2021 · 2nd cut --> 4 pieces. the cube is then cut into 27 equal sized smaller cubes. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. Aug 17, 2023 · To transform a cube into 24 identical pieces, a minimum of three cuts is required. Thus, on comparing from the above equation, we get that, The total number of minimum cuts = 1 + 3 + 4 = 8 . If we cut once on one face and another on the other face it becomes 4 identical Nov 3, 2023 · To achieve this, we need to make sure each cut intersects the previous cuts at the same points. Oct 24, 2019 · Answer: 11 cuts. By executing this logic till the 12th cut, you can obtain the maximum number of pieces. 8 d. We start to notice a pattern: if we have a cube we want to split into n pieces, we look at the prime factorization of n, and subtract one from each prime factor to find the number of cuts we need. 48 pieces; 150 pieces; 210 pieces; 294 pieces; 343 pieces Find the ratio between the maximum and the minimum number of pieces that can be obtained by cutting a cube 16 times. SOLUTION: As we are given, We need to cut a cube into 60 identical pieces. ⇒ It can be concluded that 'n' cuts made along one plane will have 'n + 1' pieces. Mar 16, 2024 · A cube is to be cut into 8 pieces of equal size and shape Here each cut should be straight and it should not stop till it reaches the other end of the cube The minimum number of such cuts required? VIDEO ANSWER: If we take the number 30 and do the prime factorization well, we get 2 times 2 times 3 times 3 times 7 times 7. What is the minimum number of cuts required to cut a cube into (i) 80 pieces? (ii) Directions for 120 pieces? (iii) faces of a cube are painted green, second pair of adjacent 125 pieces? (iv) faces blue, and a third pair of adjacent faces red. 343 smaller pieces have no painted face Additional Info : For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1, Number of cubes with 0 side painted Q. Since the number 32 is 25, we are looking for a way to split the cube into 25 smaller Oct 13, 2010 · Claim: Minimum number of cuts is at most (r + k - 1)^3. First, each cut can at most double the number of pieces you have. 1 Example 1: Find the least number of cuts required which can cut a cube into 24 identical pieces? 1. This process involves strategic slicing to achieve equal and uniform segments. This gives you 24 identical elongated cuboids with (6–1) + (4–1) or 8 cuts. The minimum number of cuts required to cut a cube into 32 identical pieces is calculated considering each cut through the cube. Step-by-step explanation: Factorise 1331 in form of a*b*c where a, b, and c are as close as possible then subtract 1 from each multiplier and add them. 48 pieces; 150 pieces; 210 pieces; 294 pieces; 343 pieces Jan 10, 2024 · The minimum number of cuts required to divide a cube into 32 identical pieces is 9. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger sizes. ] The carpenter could rearrange the pieces after Oct 5, 2020 · Number of smaller cubes on each edge, i. 12 x 2. [Image of a three-inch cube with six cuts through it. The minimum number of cuts needed is 7. So the 2nd cut can make 1 + 2 = 3 pieces. May 10, 2020 · Cubes Part-3 | Minimum no of cuts required to cut a cube in N pieces | CAT, XAT, SNAP, NMAT, CMAT Oct 10, 2018 · Ask Question. In case of 3*5*8 → No. Since the student wishes to divide the cube into smaller cubes of identical size, we have to find a way to achieve 32 equal volumes. a, b, c is the no of pieces when cut from one of the dimensions of 3D respectively. 23 cuts. The least possible number of cubes will be The least possible number of cubes will be Easy Nov 23, 2019 · 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. n = X/Y = 10/2 = 5, i. Lastly, the number of cubes having no faces painted can be found by subtracting the sum of the painted cubes from the total number of smaller cubes. Jun 8, 2022 · Given a square piece and a total number of cuts available n, Find out the maximum number of rectangular or square pieces of equal size that can be obtained with n cuts. For the plane case (usual cake without horizontal cut), I'd like to say $2n$, but you can do much more, cutting a bit away from the center : with 3 cuts you get not 6 but Nov 4, 2021 · Minimum number of cuts = a + b + c = 24 . There is only a rough drawing. 4th Day: Takes back cuts of 1 and 2 units. Step-by-step explanation: The easiest case is slicing down through the top to get 6x4 vertical cuboids. Mar 21, 2022 · Fifth cut: The fifth cut can be made perpendicular to the first four cuts, dividing each of the 16 identical pieces into two identical pieces. All cuts are parallel to some face. 216 c. Therefore, minimum number of cuts required = 12 Oct 22, 2019 · ( x + 1 ) ( y + 1 ) ( z + 1 ) = Total number of cuts. Previous Question: What is the least number of Identical cuboids, each of dimensions 2cm*4cm*5cm, that are required to form a cube Next Question: What is the maximum number of pieces into which a cube can be cut by 11 cuts. The allowed cuts are horizontal and vertical cut. 6 b. Apr 2, 2024 · A cube is to be cut into 8 pieces of equal size and shape. There are 3 and 7 in a cube form … Jan 23, 2020 · For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1) (7 + 1) (7 + 1) = 7 x 8 x 8 = 448. So, 40 = 2 × 4 × 5. Therefore, the maximum number of identical pieces a cube can be cut into by 12 cuts is 16. Then there will be $ 9 $ identical figures obtained as a result. Systematically, how many ways can you factor 24 into 1, 2, or 3 factors? (3 for 3 dimensions) Feb 27, 2022 · How many cuts are required to cut a cube into 512 pieces? 1. What is the maximum possible number of pieces into which a cube can be cut by (i) 16 cuts (ii) 11 cuts (iii) 15 cuts (iv) 19 cuts (v) 20 cuts How many cuts are required to cut a cube into 512 pieces? Feb 21, 2023 · Solution For A cube is painted and cut into 512 smaller but identical pieces by making the minimum possible nun of cuts. Apr 26, 2024 · The maximum number of identical pieces a cube can be cut into by 3 cuts is 8. How many cuts are in a cube? Cube cutting is an important concept as questions are frequently asked from this topic in a number of competitive exams. Nov 30, 2020 · GIVEN: A cube needs to be cut into 60 pieces. So, the correct option is 2. First, divide the cube via 3 planes into 8 cubes and then, these 8 cubes will be cut again into 100 pieces. Sep 4, 2023 · 4 cuts are required to cut a cube into 100 identical pieces. It is clear that this can be done with 6 cuts to the original cube (2 in the x, 2 in the y, 2 in the z). 1st Day: Employer gives 1 unit cut. Oct 4, 2023 · The 1st cut can cut a cube into 2 pieces. TO FIND: Number of cuts. Then we cut another three cut on the same surface but perpendicular to the first cuts. What is the minimum possible number of cuts required to cut a cube into. This is because each of the six sides of the cube must be cut in order to create the 27 smaller cubes. How many smaller pieces have exactly three painted faces? (18 (2) 16 (3) 32 (4) 48 7. What is the maximum number of identical pieces a cube can be cut into by 15 cuts. VIDEO ANSWER: We have a cube here as a welcome. 6th cut --> only cut 18 of the 32 pieces --> 50 pieces. A solid cube has been painted yellow, blue and black on pairs of opposite faces. What is the minimum number of cuts required to cut a cube into 100 pieces? 7. For the cuts has to be minimum, 40 has be factorized to the near factors. Slice the top into 12 slices and the cut the middle once horizontally. Verified by Toppr. Find the minimum number of cuts required to get 120 smaller pieces cuboids or cubes from a large cube?Q. What is the minimum number of cuts required to cut a cube? Sep 20, 2016 · The first cut divides it into two pieces, the second cut divides it into four pieces. Asked 5 years, 7 months ago. 2. the minimum number of cuts required to cut a cube into 216 identical pieces of cube is 36 Nov 20, 2023 · Directions for (Q. The fourth cut also can't cut all the 7 pieces, so the final answer is surely less than 14. 9 How many least cuts are required to divide a cube into 210 equal pieces without putting the pieces one on another? (1) 10 3) 20 \ ( ( \) (2) \ ( ) 15 \quad 210 \) 4) 25. So the correct answer is option B. Now we have 32 identical pieces, but we have exceeded the maximum number of pieces that can be obtained by 12 cuts. There are 3 sides to this thing. So the number of pieces will be (5 + 1) (6 +1) (6 + 1) = 294. Step-by-step explanation: hope it's help Mar 4, 2021 · For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1) (7 + 1) (7 + 1) = 7 x 8 x 8 = 448. What is the smallest number of cuts required to create 64 unit cubes from a 4 by 4 by 4 unit block of wood? I thought that maybe we could make 3 cuts in the x, y, and z direction, but that would be the wrong answer of 9. Explanation: Jun 21, 2015 · What is the minimum number of cuts required to divide a cube into 27 smaller equal cubes? What is the minimum number of cuts required to divide a cube into 27 smaller equal cubes? 3 X 3 X 3 Rubik Cube is Answer for thi question. 70 3. 3 Example 3: A cube of side 20 cm is of blue color with a 4 cm wide yellow strip along all the sides on all the faces. VIDEO ANSWER: There is a cube here, a welcome. Therefore, the required answer is 216 – (8 + 48 + 96) = 64 cubes. It remains to show that 7 cuts suffices. First we cut 3cut on the surface. 64 d. 511 2. Therefore correct option is B. 24 cuts. ) 8. When one of the cornal is sliced, we get an image or a shape, as shown here, and this is not drawn to scale. 150. Each cut is made parallel to some surface of the cube. So, 6 is the minimum. What is the maximum number of identical pieces a cube can be cut into by 73 cuts. "A cube is to be cut into 27 smaller cubes (just like a Rubik's Cube). Assuming you placed the pieces strategically every time, the last 18 pieces you need to cut are exactly 2/50th of the total length and the 14 others are 1/50th. 11 + 1 = 12 cuts. Again, by cutting the cube along the perpendicular, it will be divided into 8 parts. 7 c. 2 Example 2: Find the maximum number of smaller pieces with 19 cuts on a cube? 1. Minimum number of pieces is 20 + 1 = 21. If he wants to maximize the number of identical diamond pieces making same number of n cuts to it. What is the minimum possible number of cuts required to cut a cube into 294 pieces? Here, we can split 17 as 5, 6 and 6 which is the most equally distributed case. Explanation: To cut a cube into identical pieces, it is important to understand that each piece should have equal dimensions. NTSE Question Papers: NTSE Select Another Category Select Another Topic. As there are 6 such faces, the number of such smaller cubes will be 16*6 = 96. —What is the minimum possble number of cuts required to cut a cube into 180 pteces? is the minimum possible number of cuts required to cut a cube into (i) 48 pieces (i) 150 pieces (iii) 210 pieces (iv) 294 pieces (v) 343 pieces Cubes 60 -s ßqa- Previous Question: What is the minimum number of cuts required to cut a cube into 8 pieces Next Question: 9 years ago A's age and B's age were in the ratio of 5:7. Now, assuming that you can arrange the pieces however you like before doing a cut, what is the minimum number of cuts required to obtain the 27 smaller cubes? We would like to show you a description here but the site won’t allow us. Explanation for n=6. 6. It's the same as the cake number problem and follows the formula $(n^3+5n+6)/6$ The minimum number of cuts required to cut a three-inch cube into 27 one-inch cubes is six. एक बड़े घन से 120 छोटे टुकड़े घन या घनाभ प्राप्त करने के लिए उस बड़े घन पर कम से कम कितने कट लगाने होंगे ? Dec 13, 2022 · Find an answer to your question What is the minimum number of cuts required to cut a cube into 50 identical pieces? a. 180 d. When 1 of the cornal is sliced, we get an image or a shape, as shown here, as this is not drawn to scale. When one of the corners of… VIDEO ANSWER: If we have 7 cakes and each of them is cut into 8 equal pieces, how many pieces will we have? If we divide one of our cakes into 8 equal pieces, we have 7 of these, and if we have 7 of these, we can figure out the number. , We need factors that are closest to each other → 3*5*8, 4*5*6. (here X = 10 and Y = 2). Step-by-step explanation: The factors of 45 is 3×3×5. May 22, 2024 · And, if we cut a cube two times along x-axis and two times along y-axis. ⇒ With 3 cuts, there will be a total of 8 cubes. Note that 1 cut = 2 parts of cube, 2 cut = 3 parts and so on. Therefore, you will need to make at least 7 cuts (since $2^6 = 64 < 100$ while $2^7 = 128 > 100$). 6 x 4: slice the top in 2 directions into 6 and 4 slices. In case of 4*5*6 → No of cuts = (4-1) + (5-1) + (6-1) = 12. Then reassemble into the original cube position and 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. 3rd cut --> 8 pieces. Mar 5, 2018 · Click here 👆 to get an answer to your question ️ What is the least number of cuts required to cut the cube into 24 identical pieces? (A) 2 (B) 4 (C) 6 (D) 8 Dec 15, 2019 · But if you weren't allowed to rearrange it and some force were holding the watermelon pieces together as you cut, the answer would be $176$. 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 If the first cut would be smaller, you'd have to reach an asymmetrical point to get a pentagon which again would leave you with two distinct and unequal side lengths. After that, in order to maximize the number of slices, each line cut that you make should intersect each other line cut previously made. 252 : 17 b. Make the cut along the plane x=3. So, you need one cut to get each face. Distributing the cuts evenly gives us (5 + 1)^3 = 6^3 = 216 pieces. Jun 26, 2017 · Think of it this way: A cake with no slices has $1$ piece. Cubes For CAT 2023 by Ravi Prakash Find the number of pieces obtained when a cube is cut by six cuts. each edge has to be divided into 5 parts. 5th cut --> 32 pieces. Oct 8, 2022 · How many cuts are required to cut a cube into 512 pieces? 4. Q. Now, assuming that you can arrange the pieces however you like before doing a cut, what is the minimum number of cuts required to obtain the 27 smaller cubes? Aug 24, 2007 · Then, even employing the optimal policy to get at least 27 cubes, there will be at least one central cube, in such way that none of its faces shares any external face. When you draw the first line cut, you cut it into $2$ pieces. e. How many smaller pieces have exactly two painted faces? (1) 40 (2) 48 ) 60 (4) 15 8. Nov 19, 2019 · 30 cuts that must be given on a bigger cube so that one can get 1331 smaller identical pieces. a. A cuboidal block of 6 c m × 9 c m × 1 2 c m is cut up into an exact number of equal cubes. 64 : 3 1. Advertisements. x At least, with one cut (line cut, of course) you can only double the number of parts, so $2^n$ is an easy upper bound, and the previous argument should work properly written. The following sequence of cuts works: Cut the stick into a length of 64 inches and a length of 36 How many smaller cubes have only two of their faces painted black? Question. Explanation: To determine the minimum number of cuts required to cut a cube into 32 identical pieces, we can use the fact that the cube needs to be divided into smaller cubes. Number of smaller cubes = n 3 = 5 3 = 125 (Basically, it’s length × Again, by cutting the cube along the perpendicular, it will be divided into 8 parts. What is the minimum number of cuts required to cut a cube into 46 identical pieces? How many pieces will result in cutting an oval 12 times? The surface of a cube is painted red and blue, 3 sides of each color. 21 4. Jan 19, 2023 · The employer can pay for seven days by making 2 cuts in a way that he has 3 rods of size 1, 2 and 4. 3. You Have do 4 cut to create same size of 27 cubes. Hence we have 7 pieces. 353. If we cut it once it turns into 2 identical pieces. 21 : 5 c. tb iq ln st mc jk df pp qs fn