Mastering Mental Ability: Cube and Dice

We see a problem of dice and cubes. There are three types of problems being discussed, and shortcuts to solve them are provided.

The first problem, TYPE I, starts with 2 positions of a dice. The question is this:

“Two positions of a dice are shown below. If 1 is at the top, which number will be at the bottom?”

Here since we can see that 2 and 3 are adjacent to 1, which means they cannot be opposite to 1. So, the possibilities are 6,4, or 5. Since there are 3 different possibilities with no clues of what is located where, it is impossible to answer this question.

The second problem, TYPE II, also involves two positions of a dice but in a different arrangement.

In this problem, we can see that 6 and 5 are adjacent to 3. Which leaves only one possibility to be on the opposite side of 3, which is 4. But what about the numbers opposite to 1,2, 6, and 5?

Writing these numbers in clockwise or anti-clockwise directions thanks to the common number 3 gives us the answers.

1 is opposite to 6.

2 is opposite to 5.

Hence, thanks to type II we know that a common number can help us use the clockwise/anti-clockwise method to find the opposite sides.

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