In a dice, each face is numbered as follows:
1) 2 is opposite to 6
2) 3 is opposite to 5
3) 4 is opposite to 1
Which of the following is definitely false?
A) 4 is not adjacent to 3 and 5
B) 4 is adjacent to 5
C) 4 is adjacent to 6
D) 4 is adjacent to 3
Dice Opposite Faces Analysis
The problem describes the pairs of opposite faces on a standard six-sided die.
- The face opposite to 2 is 6.
- The face opposite to 3 is 5.
- The face opposite to 4 is 1.
This means the pairs of opposite faces are (2, 6), (3, 5), and (1, 4).
Identifying Adjacent Faces for Number 4
A standard die has 6 faces. The faces adjacent to any given face are all the other faces except the one opposite to it.
For face 4, the opposite face is 1.
Therefore, the faces adjacent to face 4 are all the remaining faces: 2, 3, 5, and 6.
Evaluating the Options
We need to find the statement that is definitely false. Let's examine each option:
- Option A: 4 is not adjacent to 3 and 5
Based on our analysis, 4 *is* adjacent to both 3 and 5. This statement claims the opposite, making it definitely false. - Option B: 4 is adjacent to 5
Since 5 is not opposite to 4 (only 1 is), 5 must be adjacent to 4. This statement is true. - Option C: 4 is adjacent to 6
Since 6 is not opposite to 4 (only 1 is), 6 must be adjacent to 4. This statement is true. - Option D: 4 is adjacent to 3
Since 3 is not opposite to 4 (only 1 is), 3 must be adjacent to 4. This statement is true.
Conclusion on False Statement
The only statement that contradicts the established adjacency rules for face 4 is Option A.
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?
