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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 at least two coloured red faces each ?
  • a)
    0
  • b)
    32
  • c)
    64
  • d)
    128
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Directions to Solve ...
64 and 64 cubes of both types of cubes are such who have at least two coloured faces red each.
Therefore, total number of the required cubes is 128.
This question is part of UPSC exam. View all LR courses
Most Upvoted Answer
Directions to Solve ...
Given Information:
- There are 128 cubes in total.
- 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:
- The number of cubes that have at least two coloured red faces each.

Solution:
Let's first find the number of cubes that have exactly two red faces each.

Number of cubes with two red adjacent faces = 64
Number of cubes with one red face and one green face = 64
Total number of cubes with at least two red faces = 64 + 64 = 128

But we need to subtract the cubes that have both red and blue faces, as they are counted twice in the above calculation.

Number of cubes with two red adjacent faces and two blue adjacent faces = 64
Therefore, the number of cubes that have at least two coloured red faces each = 128 - 64 = 64

Hence, the correct answer is option (c) 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 at least two coloured red faces each ?a)0b)32c)64d)128Correct answer is option 'D'. Can you explain this answer?
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