In this post we will see solved problems of cubes and dice. All the questions are solved in as comprehensive manner as possible so that student with poor math background can even understand the concept.
Problems on dice are all about find relation between the different image of dice give. These type of questions tests your analytical capability and demand the right answer within limited time frame.
I hope this post will help you develop some skill to solve these kind of problems in competition examination
Logical Reasoning Problems on Cubes and Dice
Q1. Two positions of a cube are given. Based on them find out which number is found opposite number 1 in the given cube
Solution-In first cube 1 is adjacent to 6 and 2
And in second cube 6 and 2 are adjacent to 3
So from above two views of cubes 1 is opposite to 3
Here our answer is 3
Q2. In a solid cube which is made up of 27 small cubes two opposite sides are painted red two painted yellow and other two with white how many cubes have two colors?
According to the question our figure is
So our cube is made up of 27 cubes and having different colors
So below dotted points show the cubes which has only two colors
Here in each level we get four such cubes which have two colored surface
So total colored surfaces are 4×3=12
So our answer is 12
Q3. In a solid cube made up of 27 small cubes, two opposite sides are painted red, two opposite sides yellow and two other sides white. How many small cubes have the colors yellow and white alone in them?
According to the question our figure is
Here the cubes of a middle row or level 2 will have no red color
And in level 2 at mid of edge we get such a cube which has only white and yellow color
So total numbers of only white and yellow colored cubes are = 4(total number of vertical edge in level 2 = 4 )
So here 4 is our answer
Q4. Three positions of a dice are given below. Identify the number on the face opposite to 6
Solution– In first view of cube 6 is adjacent to 3 and 2
And in second view of cube 6 is adjacent to 3 and 5
So clearly here 5 is opposite to 2
And in second view 5 is adjacent to 6 and 3
And adjacent to 4 and 3 in third view
So from here we say that 4 is opposite to 6
Here 4 is our answer
(05) A solid cube of 4 inches has been painted Red, Green, and Black on pair of opposite faces. It has been cut into one inch cubes. How many cubes have only one face painted that too only red?
According to question our figure is shown below which is cut into 1 inches cubes
So total number of cubes = 43=64
Here we have to find those cubes which has only red painted
So here we find middle cubes of level 2 and 3 (in front side and back side) have only red colors shown as dotted points
So total number of red colored cubes in front side and back side are 4+4=8
Here 8 is our answer
(06) Identify the number when top is 5 what will be at bottom?
Solution-In this type of question where dice view is tree or more we have to find the digit which is more repeating among other digits and after that find their adjacent.
Here we get 3 is in first second and fourth dice and its adjacent are 4,2,1,5
(Here same colors shows that they are opposite faces)
So it is clear that 6 is opposite to 3 and we eliminate digits 6 and 3 from option
Now after that 5 is adjacent to 1, 3, 2 so its opposite is 4
So 4 is our answer
Q7. Study the following figures and find out the number opposite to 2.
Solution-In this type of question where dice view is tree or more we have to find the digit which is more repeating among other digits and after that find their adjacent.
Here we get 3 is in first second and third dice and its adjacent are 6, 2, 5, 4
(Here same colors shows that they are opposite faces)
So it is clear that 1 is opposite to 3 and we eliminate digits 1 from option
Now after that 6 is adjacent to 5, 3, 2 so its opposite is 4 so eliminate digits 4 and 6 from option
Here 5 lies opposite to 2
So 5 is our answer
Q8. A dice is thrown four times and its four different positions are given below. Find the number on the face opposite the face showing 2
Solution-In this type of question where dice view is tree or more we have to find the digit which is more repeating among other digits and after that find their adjacent.
Here we get 2 is in first second and fourth dice and its adjacent are 3, 4, 1, 6
So it is clear that 2 is opposite to 5
(Here same colors shows that they are opposite faces)
Q9. How many cubes are there in this diagram?
(a) 10 (b) 8
(c) 16 (d) 12
Solution – The whole structure is hollow cuboid
So counting at corners (red color)we get 4 cubes
And at middle of edge(blue color) we get two cubes, so for four sides total cubes are = 2×4=8
So total number of cubes are = 4+8 =12
Here 12 is our answer
(10) How many cubes are there in this figure
(a) 69 (b) 180
(c) 144 (d) 84
Solution-So here we have to find total cubes in big cuboid
So we multiply the numbers of column from each view that is
Front view = 6 column
Top view = 6 column
Side view = 4 column
So total number of cubes = 6×6×4 =144
Here 144 is our answer
(11) Which of the following cubes can be created by folding the given figure?
Solution-From figure it is clear that F is adjacent to B
Here E is opposite to B, so eliminate option (a)
E is opposite to C, so eliminate option (c)
A is opposite to D, so eliminate option (d)
Here option (b) is our answer
Q12. Four positions of a dice are given below. Identify the number at the bottom when top is 6.
(a) 1 (b) 3
(c) 4 (d) 5
Solution-In this type of question where dice view is tree or more we have to find the digit which is more repeating among other digits and after that find their adjacent.
Here we get 4 is in second third and fourth dice and its adjacent are 1, 2, 5, 6
(Here same colors shows that they are opposite faces)
So it is clear that 4 is opposite to 3 and we eliminate digits 4 and 3 from option
Now after that 2 is adjacent to 1, 3, 4, 6 so its opposite is 5, now eliminate digit 5 from option
So we get digit 1 is opposite to 6
So 4 is our answer
(13) From the given options, which figure can be formed by folding the figure in the question?
Solution-From figure it is clear that
1 is opposite to 5, so eliminate option (b) and option (d)
6 is opposite to 3, so eliminate option (c)
2 is opposite to 4
