Dices & Cubes — PYPs

Read off every face that shares a view with 3. The first die shows 3 with 2 and 6, the third shows it with 6 and 1, and the fourth shows it with 5 and 1 - so $2, 6, 1$ and $5$ are all adjacent to 3.

That leaves only one number unaccounted for, and a face can only be adjacent or opposite. Hence 4 is opposite 3, which is Option 2.

The Setup: We are dealing with a standard $n \times n \times n$ painted cube problem. The total number of cubes is 27, which means $n^3 = 27$, so $n = 3$. We can dox the exact counts using the standard formulas.

Step 1: Stat-check the formulas
* 3 faces painted (Corners): Always exactly 8. (Statement D is True)
* 2 faces painted (Edges): $12 \times (n - 2) = 12 \times (3 - 2) = 12$. (Statement C says six, so C is False)
* 1 face painted (Face centers): $6 \times (n - 2)^2 = 6 \times (1)^2 = 6$. (Statement A is True)
* 0 faces painted (Inner core): $(n - 2)^3 = (1)^3 = 1$. (Statement B is True)

Step 2: Secure the final bag
Statements A, B, and D are perfectly accurate.

Final Answer: A, B and D only