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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?
Most Upvoted 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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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.
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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 2025 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 2025 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 2025 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 2025 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?.
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