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Directions to Solve
There are 128 cubes with me which are coloured according to two schemes viz.
  1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
  2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.
Question -
How many cubes have two adjacent blue faces each ?
  • a)
    64
  • b)
    32
  • c)
    0
  • d)
    128
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Directions to Solve ...
Second 64 cubes are such each of whose two faces are blue.
This question is part of UPSC exam. View all LR courses
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Directions to Solve ...
Given Information:
- 64 cubes have two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
- 64 cubes have two adjacent blue faces and one red and other green on their opposite faces, while red on the rest.

To find: Number of cubes with two adjacent blue faces.

Solution:
- Out of 64 cubes with two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest, only the blue faces are of our interest. So, we need to find the number of cubes with blue faces adjacent to each other.
- Similarly, out of 64 cubes with two adjacent blue faces and one red and other green on their opposite faces, only the blue faces are of our interest. So, we need to find the number of cubes with two adjacent blue faces.
- Now, let’s consider the cubes with two red adjacent faces. These cubes will have green faces opposite to each other. Therefore, we can arrange these cubes in a way that the green faces are touching each other, forming a block of 64 cubes.
- Similarly, we can form a block of 64 cubes with two adjacent blue faces by arranging the cubes with two adjacent blue faces in a way that the red faces are touching each other.
- Now, we can mix these two blocks of 64 cubes each to get a total of 128 cubes.
- As both the blocks are arranged in a way that the faces of the same color are touching each other, the cubes with two adjacent blue faces will be present only in the second block of 64 cubes.
- Therefore, the number of cubes with two adjacent blue faces is 64.
- Hence, the correct option is (a) 64.

Answer: a) 64
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Directions to Solve There are 128 cubes with me which are coloured according to two schemes viz.64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up. Question - How many cubes have two adjacent blue faces each ?a)64b)32c)0d)128Correct answer is option 'A'. Can you explain this answer?
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