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Aptitude Training - PROBLEMS ON CUBES
The document discusses problems involving cubes that are painted different colors on their faces and then cut into smaller identical cubes. It provides the answers to questions about counting the number of smaller cubes with a given number of faces of each color. For a cube cut into 216 smaller cubes where 3 pairs of adjacent faces are each painted a single color, there are 72 cubes with no red paint, 44 with at least two colors, 72 with only red or blue, 14 with only red and blue, and 18 with red and blue. For a cube cut into 343 smaller cubes where 3 faces are each a different color, there are 43 painted cubes total, 1 with 3 faces painted, 18 with 2 faces painted, 75 with 1 face painted, and
Aptitude Training - PROBLEMS ON CUBES
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- 2. 1. 64 smalleridentical cubes are arranged to form a larger cube. How many such similar type of smaller identical cubes are required to completely cover the larger cube Number of smaller cubes with 3 faces open ? Number of smaller cubes with 2 faces open ? Number of smaller cubes with 1 faces open? Number of smaller cubes with 0 faces open? 2. A cube is painted on all its faces with red color. The cube is now cut into 343 smaller identical cubes? Number of smaller cubes with 3 faces open ? Number of smaller cubes with 2 faces open ? Number of smaller cubes with 1 faces open? Number of smaller cubes with 0 faces open? 3. A cube is painted on 3 pairs of opposite faces with same color red, blue , green . The cube is now cut into 216 smaller identical cubes? Number of smaller cubes with no red paint? Number of smaller cubes at least two different colors? Number of smaller cubes only red or only blue? Number of smaller cubes only red and blue? Number of smaller cubes with red and blue?
- 3. • A cubehas 6 faces, 12 edges and 8 corners • Number of smaller cubes with 3 faces open = corners = 8 • Number of smaller cubes with 2 faces open = 12 (n - 2) • Number of smaller cubes with 1 faces open = 6 • Number of smaller cubes with 0 faces open =
- 4. 64 smaller identicalcubes are arranged to form a larger cube. Number of smaller cubes with 3 faces open ? Number of smaller cubes with 2 faces open ? Number of smaller cubes with 1 faces open? Number of smaller cubes with 0 faces open? 1. Ans: => n = 4 Number of smaller cubes with 3 faces open = 8 Number of smaller cubes with 2 faces open = 12 (4 - 2) = 24 Number of smaller cubes with 1 faces open = 6 Number of smaller cubes with 0 faces open = = 8
- 5. A cube ispainted on all its faces with red color. The cube is now cut into 343 smaller identical cubes? Number of smaller cubes with 3 faces open ? Number of smaller cubes with 2 faces open ? Number of smaller cubes with 1 faces open? Number of smaller cubes with 0 faces open? 2. Ans: => n = 7 Number of smaller cubes with 3 faces open = 8 Number of smaller cubes with 2 faces open = 12 (7 - 2) = 60 Number of smaller cubes with 1 faces open = 6 150 Number of smaller cubes with 0 faces open = = 125
- 6. A cube ispainted on 3 pairs of opposite faces with same color red, blue , green . The cube is now cut into 216 smaller identical cubes? Number of smaller cubes with no red paint? Number of smaller cubes at least two different colors? Number of smaller cubes only red or only blue? Number of smaller cubes only red and blue? Number of smaller cubes with red and blue? 3. Ans : n = 6 Number of smaller cubes with no red paint = 144 Number of smaller cubes at least two different colors = 56 Number of smaller cubes only red or only blue = 64 Number of smaller cubes only red and blue = 16 Number of smaller cubes with red and blue = 24
- 7. Subscribe to : Problemsfor practice are given in the description of the video.
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- 9. 1. A cubeis painted on 3 pairs of adjacent faces with same color red, blue, green. This cube is now cut into 216 smaller identical cubes Number of smaller cubes with no red paint? Number of smaller cubes at least two different colors? Number of smaller cubes only red or only blue? Number of smaller cubes only red and blue? Number of smaller cubes with red and blue? 2. A cube is painted on 3 faces with 3 different colors red, green and blue. This cube is cut into 343 identical cubes. Number of smaller cubes painted? Number of smaller cubes with 3 faces painted ? Number of smaller cubes with 2 faces painted? Number of smaller cubes with 1 faces painted? Number of smaller cubes with 0 faces painted?
- 10. 1. A cubeis painted on 3 pairs of adjacent faces with same color red, blue, green. This cube is now cut into 216 smaller identical cubes Number of smaller cubes with no red paint? Number of smaller cubes at least two different colors? Number of smaller cubes only red or only blue? Number of smaller cubes only red and blue? Number of smaller cubes with red and blue? Ans : n = 6 Number of smaller cubes with no red paint = 72 Number of smaller cubes at least two different colors = 44 Number of smaller cubes only red or only blue = 72 Number of smaller cubes only red and blue = 14 Number of smaller cubes with red and blue = 18
- 11. 2. A cubeis painted on 3 faces with 3 different colors red, green and blue. This cube is cut into 343 identical cubes. Number of smaller cubes painted? Number of smaller cubes with 3 faces painted ? Number of smaller cubes with 2 faces painted? Number of smaller cubes with 1 faces painted? Number of smaller cubes with 0 faces painted? Ans: n = 7 Number of smaller cubes painted = 43 Number of smaller cubes with 3 faces open = 1 Number of smaller cubes with 2 faces open = 18 Number of smaller cubes with 1 faces open = 75 Number of smaller cubes with 0 faces open = 300
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