Question

Arnav rolls an ordinary dice and gets a '3' on the face of the dice. What shall be the number if the number that is on the side that is exactly opposite to the face of the dice is multiplied by itself four times?

• A. 12
• B. 81
• C. 256
• D. 1296
  (E) 256
• E. 256

Hint:

"Ordinary," "Standard," and "Fair" dice all follow the rule that the sum of opposite faces is 7. Memorize powers of 4 for speed: $4^1=4, 4^2=16, 4^3=64, 4^4=256$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An "ordinary dice" is synonymous with a "standard dice." In such a dice, the sum of opposite faces is always 7.

Step 2: Key Formula or Approach:
1. Opposite face = $7 - \text{Current face}$.
2. Result = $(\text{Opposite face})^4$.

Step 3: Detailed Explanation:
1. Arnav gets a '3'. 2. The number on the opposite face is $7 - 3 = 4$. 3. We need to multiply this number (4) by itself four times: \[ 4 \times 4 \times 4 \times 4 = 4^4 \] \[ 4^1 = 4 \] \[ 4^2 = 16 \] \[ 4^3 = 64 \] \[ 4^4 = 256 \]

Step 4: Final Answer:
The resulting number is 256.