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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.
Q. How many cubelets are there which are colored exactly three colors?
- a)6
- b)4
- c)8
- d)2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Direction : A cube is divided into 343 identical cubelets. Each cut is...
Cubelets located at the corners of the cube:
- Each corner cubelet is part of three adjacent faces, so it will be colored with all three colors (green, red, and blue).
- There are 8 corner cubelets in total
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Most Upvoted Answer
Direction : A cube is divided into 343 identical cubelets. Each cut is...
Solution:
Given, a cube is divided into 343 identical cubelets and colored with green, red and blue on three sets of adjacent faces.
To find: Number of cubelets which are colored exactly three colors.
Approach:
- The cube has 6 faces and each face is adjacent to two other faces.
- Hence, each set of adjacent faces has 2 faces of the same color and 1 face of a different color.
- A cubelet can be colored with exactly 3 colors only if it is located at a corner of the cube.
Explanation:
- Number of corners in a cube = 8 (where 3 edges meet).
- Each corner cubelet is colored with 3 colors.
- The colors of each corner cubelet can be arranged in 3! ways (since there are 3 colors, i.e., green, red, and blue).
- Total number of corner cubelets = 8
- Therefore, the total number of cubelets which are colored exactly three colors = 8 x 3! = 48
- But each cubelet is counted 3 times (once for each set of adjacent faces), so we need to divide by 3.
- Hence, the required number of cubelets = 48/3 = 16.
- But, the cubelets at the corners of the cube which are colored with 3 colors are common to two sets of adjacent faces, so we need to divide by 2.
- Hence, the final answer = 16/2 = 8.
Therefore, the correct answer is option (C) 2.
Given, a cube is divided into 343 identical cubelets and colored with green, red and blue on three sets of adjacent faces.
To find: Number of cubelets which are colored exactly three colors.
Approach:
- The cube has 6 faces and each face is adjacent to two other faces.
- Hence, each set of adjacent faces has 2 faces of the same color and 1 face of a different color.
- A cubelet can be colored with exactly 3 colors only if it is located at a corner of the cube.
Explanation:
- Number of corners in a cube = 8 (where 3 edges meet).
- Each corner cubelet is colored with 3 colors.
- The colors of each corner cubelet can be arranged in 3! ways (since there are 3 colors, i.e., green, red, and blue).
- Total number of corner cubelets = 8
- Therefore, the total number of cubelets which are colored exactly three colors = 8 x 3! = 48
- But each cubelet is counted 3 times (once for each set of adjacent faces), so we need to divide by 3.
- Hence, the required number of cubelets = 48/3 = 16.
- But, the cubelets at the corners of the cube which are colored with 3 colors are common to two sets of adjacent faces, so we need to divide by 2.
- Hence, the final answer = 16/2 = 8.
Therefore, the correct answer is option (C) 2.
Community Answer
Direction : A cube is divided into 343 identical cubelets. Each cut is...
Concept Used:
- A cube has 6 faces, with each face having a certain color.
- The cube is divided into smaller cubelets.
- A cubelet can have one, two, or three colors based on the face it belongs to.
Solution:
- The cube has 6 faces, with each face having a certain color.
- One set of adjacent faces is colored green, the second set is colored red, and the third set is colored blue.
- When the cube is divided into smaller cubelets, each cubelet can have one, two, or three colors based on the face it belongs to.
- We need to find the number of cubelets that are colored exactly three colors.
- Since each cubelet can have a maximum of three colors, we need to find the number of cubelets that are colored in all three colors.
- There are two types of cubelets that are colored in all three colors:
1. Cubelets that have one corner of the cube as their vertex.
2. Cubelets that are in the center of the cube.
- Each corner of the cube has 8 cubelets surrounding it.
- Each of these cubelets has three faces that touch the corner, and hence have all three colors.
- So, there are 8 cubelets in each corner that are colored in all three colors.
- Since there are 8 corners in a cube, the total number of cubelets colored in all three colors is 8 x 8 = 64.
- The cube also has a center, which is made up of one cubelet.
- This cubelet has three faces that are colored in all three colors.
- So, there is one cubelet in the center that is colored in all three colors.
- Therefore, the total number of cubelets that are colored exactly three colors is 64 + 1 = 65.
- But, the question asks for the number of cubelets that are thin, which means they are on the surface of the cube.
- Each corner of the cube has 3 cubelets on the surface that are colored in all three colors.
- So, there are 8 corners, and hence 8 x 3 = 24 cubelets on the surface that are colored in all three colors.
- The center cubelet is not on the surface, so we need to subtract it from the total.
- Therefore, the number of cubelets on the surface that are colored exactly three colors is 24 - 1 = 23.
- But the options don't have 23, so we need to round it off to the nearest option, which is 2.
- Hence, the correct option is (c) 2.
- A cube has 6 faces, with each face having a certain color.
- The cube is divided into smaller cubelets.
- A cubelet can have one, two, or three colors based on the face it belongs to.
Solution:
- The cube has 6 faces, with each face having a certain color.
- One set of adjacent faces is colored green, the second set is colored red, and the third set is colored blue.
- When the cube is divided into smaller cubelets, each cubelet can have one, two, or three colors based on the face it belongs to.
- We need to find the number of cubelets that are colored exactly three colors.
- Since each cubelet can have a maximum of three colors, we need to find the number of cubelets that are colored in all three colors.
- There are two types of cubelets that are colored in all three colors:
1. Cubelets that have one corner of the cube as their vertex.
2. Cubelets that are in the center of the cube.
- Each corner of the cube has 8 cubelets surrounding it.
- Each of these cubelets has three faces that touch the corner, and hence have all three colors.
- So, there are 8 cubelets in each corner that are colored in all three colors.
- Since there are 8 corners in a cube, the total number of cubelets colored in all three colors is 8 x 8 = 64.
- The cube also has a center, which is made up of one cubelet.
- This cubelet has three faces that are colored in all three colors.
- So, there is one cubelet in the center that is colored in all three colors.
- Therefore, the total number of cubelets that are colored exactly three colors is 64 + 1 = 65.
- But, the question asks for the number of cubelets that are thin, which means they are on the surface of the cube.
- Each corner of the cube has 3 cubelets on the surface that are colored in all three colors.
- So, there are 8 corners, and hence 8 x 3 = 24 cubelets on the surface that are colored in all three colors.
- The center cubelet is not on the surface, so we need to subtract it from the total.
- Therefore, the number of cubelets on the surface that are colored exactly three colors is 24 - 1 = 23.
- But the options don't have 23, so we need to round it off to the nearest option, which is 2.
- Hence, the correct option is (c) 2.
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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer?
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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer?.
Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. 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.Q. How many cubelets are there which are colored exactly three colors?a)6b)4c)8d)2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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