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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 -
Which two colours have the same number of faces ?
  • a)
    Red and Yellow
  • b)
    Blue and Green
  • c)
    Red and Green
  • d)
    Red and Blue
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Directions to Solve ...
First 64 cubes are such each of whose two faces are green and second 64 cubes are such each of whose two faces are blue.
Therefore, green and blue colours have the same number of faces.
This question is part of UPSC exam. View all LR courses
Most Upvoted Answer
Directions to Solve ...
Problem Analysis

We have a total of 128 cubes, each colored according to two schemes:
- Scheme 1: 64 cubes have two red adjacent faces and one yellow and one blue on their opposite faces, while green on the rest.
- Scheme 2: 64 cubes have two adjacent blue faces and one red and one green on their opposite faces, while red on the rest.

The cubes are then mixed up, and we need to determine which two colors have the same number of faces.

Solution

To solve this problem, we need to analyze the number of faces in each color for both schemes and compare them.

Scheme 1:
- Number of cubes with red faces: 64
- Number of cubes with yellow faces: 64
- Number of cubes with blue faces: 64
- Number of cubes with green faces: 128 - (64 + 64 + 64) = 128 - 192 = -64 (negative value, which means there are no cubes with green faces in Scheme 1)

Scheme 2:
- Number of cubes with red faces: 64
- Number of cubes with blue faces: 64
- Number of cubes with green faces: 64
- Number of cubes with yellow faces: 128 - (64 + 64 + 64) = 128 - 192 = -64 (negative value, which means there are no cubes with yellow faces in Scheme 2)

From the analysis above, we can see that:
- Scheme 1 does not have any cubes with green faces.
- Scheme 2 does not have any cubes with yellow faces.

Therefore, the two colors that have the same number of faces are Blue and Green (option B).

Conclusion

In the given set of 128 cubes, the two colors that have the same number of faces are Blue and Green. This is determined by analyzing the number of cubes with each color in both Scheme 1 and Scheme 2.
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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 - Which two colours have the same number of faces ?a)Red and Yellowb)Blue and Greenc)Red and Greend)Red and BlueCorrect answer is option 'B'. Can you explain this answer?
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