In a dice, each face is numbered as follows: 1) 3 is opposite to 6 2) 4 is opposite to 5 3) 2 is opposite to 1 Which of the following is definitely false?
4 is not adjacent to 3 and 6
Dice Opposite Faces Analysis
The problem describes the opposite face pairings for a specific six-sided die:
- Face 3 is opposite to Face 6 ($3 \leftrightarrow 6$)
- Face 4 is opposite to Face 5 ($4 \leftrightarrow 5$)
- Face 2 is opposite to Face 1 ($2 \leftrightarrow 1$)
Determining Adjacent Faces
For any standard die, a face has 4 adjacent faces and 1 opposite face. We can deduce the adjacent faces from the given opposite pairs:
- Faces adjacent to 3 and 6 are {1, 2, 4, 5}.
- Faces adjacent to 4 and 5 are {1, 2, 3, 6}.
- Faces adjacent to 2 and 1 are {3, 4, 5, 6}.
Evaluating the Statements
We examine each option to find the one that is definitely false:
- Option 1: 4 is not adjacent to 3 and 6
According to our deduction, the faces adjacent to 4 are {1, 2, 3, 6}. This means 4 is adjacent to 3 and 6. Therefore, the statement "4 is not adjacent to 3 and 6" is false. - Option 2: 4 is adjacent to 2
From the list {1, 2, 3, 6}, Face 4 is adjacent to Face 2. This statement is true. - Option 3: 4 is adjacent to 1
From the list {1, 2, 3, 6}, Face 4 is adjacent to Face 1. This statement is true. - Option 4: 5 is adjacent to 3
The faces adjacent to 5 are {1, 2, 3, 6}. Face 5 is adjacent to Face 3. This statement is true.
Conclusion
The statement that contradicts the derived rules of adjacency for the given dice configuration is Option 1. Thus, "4 is not adjacent to 3 and 6" is definitely false.
Important Questions from Cube and Dice
A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each. Find the number of smaller cube having all the three faces painted.
A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each. Find the number of smaller cubes having only one face printed.
A cube of side 18 cm is painted yellow on all the faces and then cut into smaller cubes of sides 3 cm each. Find the number of smaller cubes that have only two faces painted.
A cube of side 12 cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each. Find the number of smaller cubes that have only one face painted.
Four friends J, Q, B and Z rolled the dice in alphabetical order.
The scores were:
1st round: 3, 2, 5, 2
2nd round: 1, 5, 1, 4
3rd round: 4, 2, 1, 1
If each point on the dice would get 10 points, who won the maximum points after 3 rounds?
