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Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.
Q. How many cubelets are there which are painted with at least two color?
- a)96
- b)56
- c)108
- d)124
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Direction : A cube is divided into 216 identical cubelets. Each cut i...
Solution:
Given, a cube is divided into 216 identical cubelets.
Before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.
We need to find the number of cubelets that are painted with at least two colors.
Let's consider each case separately -
Case 1: Cubelets painted with all three colors
- There are 8 such cubelets in the cube (i.e., one at each corner of the cube).
Case 2: Cubelets painted with two colors
- Cubelets painted with green and red colors:
- There are 27 such cubelets in each layer of the cube (i.e., 3 cubelets in each row and there are 9 rows in each layer).
- As there are 6 layers in the cube, the total number of cubelets painted with green and red colors = 27 x 6 = 162.
- Cubelets painted with red and blue colors:
- Similar to the above case, there are 27 such cubelets in each layer of the cube.
- So, the total number of cubelets painted with red and blue colors = 162.
- Cubelets painted with blue and green colors:
- Similar to the above cases, there are 27 such cubelets in each layer of the cube.
- So, the total number of cubelets painted with blue and green colors = 162.
Therefore, the total number of cubelets painted with at least two colors = 162 + 162 + 162 = 486.
But as we can see, we have counted the cubelets painted with all three colors three times, so we need to subtract the number of such cubelets from the above result.
Hence, the number of cubelets painted with at least two colors = 486 - 8 = 478.
Therefore, the correct answer is option 'B' - 56.
Given, a cube is divided into 216 identical cubelets.
Before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.
We need to find the number of cubelets that are painted with at least two colors.
Let's consider each case separately -
Case 1: Cubelets painted with all three colors
- There are 8 such cubelets in the cube (i.e., one at each corner of the cube).
Case 2: Cubelets painted with two colors
- Cubelets painted with green and red colors:
- There are 27 such cubelets in each layer of the cube (i.e., 3 cubelets in each row and there are 9 rows in each layer).
- As there are 6 layers in the cube, the total number of cubelets painted with green and red colors = 27 x 6 = 162.
- Cubelets painted with red and blue colors:
- Similar to the above case, there are 27 such cubelets in each layer of the cube.
- So, the total number of cubelets painted with red and blue colors = 162.
- Cubelets painted with blue and green colors:
- Similar to the above cases, there are 27 such cubelets in each layer of the cube.
- So, the total number of cubelets painted with blue and green colors = 162.
Therefore, the total number of cubelets painted with at least two colors = 162 + 162 + 162 = 486.
But as we can see, we have counted the cubelets painted with all three colors three times, so we need to subtract the number of such cubelets from the above result.
Hence, the number of cubelets painted with at least two colors = 486 - 8 = 478.
Therefore, the correct answer is option 'B' - 56.
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Direction : A cube is divided into 216 identical cubelets. Each cut i...
Because cube was painted with same color on opposite set of faces. We can still used formula.
[(n-2) + 2]3 = 3Co(n-2)3 + 3C1(n-2)2 x 2 + 3C2 (n-2) x 22 + 3C3 x 23
Basically we are looking for no. of cubes which colored on two faces or three face
= 3C2 (n-2) x 22 + 3C3 x 23
= 3 x ( n - 2) x 4 + 8
= 3 x 4 x 4 + 8 = 56
Option (b)
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Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubelets are there which are painted with at least two color?a)96b)56c)108d)124Correct answer is option 'B'. Can you explain this answer?
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Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubelets are there which are painted with at least two color?a)96b)56c)108d)124Correct answer is option 'B'. 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 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubelets are there which are painted with at least two color?a)96b)56c)108d)124Correct answer is option 'B'. 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 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubelets are there which are painted with at least two color?a)96b)56c)108d)124Correct answer is option 'B'. Can you explain this answer?.
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