Discussion
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- Question
- Find the maximum number of cuts required to get 50 pieces.
Options- A. 50
- B. 51
- C. 49
- D. None of these
- Correct Answer
- 50
ExplanationFor maximum number of cuts it has to be in one cut only, so number of cuts is 49
- 1. If total number of pieces (Smaller cubes/cuboids) is 45 then find the possible number of cuts.
Options- A. 18 or 16
- B. 8 or 12
- C. 12 or 18
- D. None of these Discuss
- 2. If total number of cuts is 20 then find the ratio of maximum and minimum of pieces that can be obtained.
Options- A. 448:63
- B. 446:21
- C. 122:21
- D. None of these Discuss
- 3. If total number of cuts is 10 then find the maximum number of pieces that can be obtained.
Options- A. 80
- B. 48
- C. 120
- D. None of these Discuss
- 4. If total number of cuts is 10 then find the minimum number of pieces that can be obtained.
Options- A. 10
- B. 11
- C. 25
- D. None of these Discuss
- 5. Find out how will the key figure (X) look like after rotation.
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 6. Find the minimum number of cuts required to get 50 pieces.
Options- A. 10
- B. 11
- C. 9
- D. None of these Discuss
- 7. How many of the cubes have 0 faces painted?
Options- A. 64
- B. 125
- C. 27
- D. None of these Discuss
- 8. How many of the cubes have 2 most faces painted?
Options- A. 144
- B. 125
- C. 96
- D. None of these Discuss
- 9. How many of the cubes have at most faces painted?
Options- A. 208
- B. 144
- C. 210
- D. None of these Discuss
- 10. How many of the cubes have at least 2 faces painted?
Options- A. 104
- B. 144
- C. 120
- D. None of these Discuss
Cubes and Dice problems
Search Results
Correct Answer: 8 or 12
Explanation:
If 45 = 1 x 1 x 45 then we require only 44 cuts in one plane.
If 1 x 3 x 15 then we require 2 cuts in one plane and 14 cuts in other plane so total number of cuts is 2 + 14 = 16.
If 1 x 5 x 9 the we require 4 cuts in one plane and 8 cuts in other plane so total number of cuts is 4 + 8 = 12
If 3 x 3 x 5 then we require 2 cuts in one plane, 2 cuts in 2nd plane and 4 cuts in 3rd plane so total number of cuts is 2 + 2 + 4 = 8.
Correct Answer: 446:21
Explanation:
For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1)(7 + 1)(7 + 1) = 7 x 8 x 8 = 448.
Minimum number of pieces is 20 + 1 = 21.
Hence required ratio is 448:21
Correct Answer: 80
Explanation:
If total number of cut is 10 then for maximum number of pieces these cuts have to be well distributed in three planes. For 10 cuts, 3,3 and 4 is the distribution of cuts.
Hence total number of pieces is
(3 + 3)(3 + 1)(4 + 1) = 4 x 4 5 = 80
Correct Answer: 11
Explanation:
If total number of cuts is 10 then minimum number of pieces is 11 when cut is made in one plane only.
Correct Answer: 4
Correct Answer: 9
Explanation:
For minimum number of cuts we will get 50 from 2 x 5 x 5 and cuts is 1 + 4 + 4 = 9
Correct Answer: 64
Explanation:
Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 0 faces painted is (6 - 2)3 = 43 = 64
Correct Answer: 96
Explanation:
Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 2 faces painted is 6(6 - 2)2
= 6 x 16 = 96
Correct Answer: 208
Explanation:
Since total number of cubes is hence in the formula we will substitute n = 6
At most 2 faces painted means number of cubes with 0 face painted + number of cubes with 1 face painted + number of cubes with 2 face painted = 64 + 48 + 96 = 208
Correct Answer: 144
Explanation:
Since total number of cubes is hence in the formula we will substitute n = 6
At least 2 faces painted means number of cubes with 2 face painted + number of cubes with 3 face painted = 96 + 8 = 104.
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