Basic Concepts to Solve Dice Problems
You should keep in mind that a cube has 6 faces. Each face has 4 adjacent faces and 1 opposite face. If you want to solve cube based problems, it’s good to advise that you should learn something about the cube and its faces.
Tricks:
If you are not able to think about the 3D cube, you can just open up the cube and create a 2D image and write down the given data on that image.
Example: Two positions of a cubical block are shown. When 5 is at the top which number will be at bottom?
Solution: We first notice the common face i.e. 3.
Then we will write down the adjacent faces, that are, 1,4,2,6.
Since we require the face opposite to 5, there is only 1 face which is not adjacent to 3, i.e. 5.
So the face opposite to 5, at the bottom, is 3.
Example: From the four positions of a dice given below, find the color which is opposite to yellow?
Solution: Since, we need to find the face opposite to yellow, we need to only find 4 adjacent faces, and the non-adjacent one is opposite to yellow.
From cube 1, orange and blue is adjacent to yellow.
From cube 3, red and blue is adjacent to yellow.
From cube 4, rose and red is adjacent to yellow.
From above 3, we can conclude that, orange, blue, red and rose are adjacent faces.
Hence, Violet is opposite to yellow.
Example: You are given three positions of dice then which face is opposite to the face with alphabet B?
Solution: Sometimes, these questions will get tricky to solve. So we will make a 2D image for this and solve accordingly.
From first 2 cubes, we can see that common face is F.
So put F at center.
From cube 1, if D is at right face then A is placed below.
From cube 2, if E is at upper face then C is at left face.
Fill the remaining block with B which is left.
You can see that F and B are non-adjacent, hence opposite to each other.
Example: In above dice example, what are the pair of opposite faces?
Solution: Creating a 2D image by solving given example.
We know that, each face has 4 adjacent faces and 1 non-adjacent face which is opposite to it.
Similar thing is applied for 2D image.
Hence, we can conclude that opposite pair of faces are: C-D, E-A and F-B.
Example: Here 4 positions of a dice are shown. Which sign will be opposite to “ * “ ?
Solution: We will start from finding the 4 adjacent faces of *
From cube 3 and 4, we find #, @ as adjacent faces
In cube 1, we can see that ^ is adjacent to both # and @.
Also, 2 adjacent sides together can be adjacent to 2 more faces only if they are opposite to each other.
Hence, ^ is opposite to *
This article is contributed by Shushank Mittal.
