assumeAssume that you have an $10\times 10$$10\times 10\times 10$ cube and many $3\times 3$ cubes in $10\times 10$ cuve if a $3\times 3$ cubess center is in boundary($10^{\text{th}}$ cube for example)$3\times 3\times 3$ cubes that are on the outside teleports to inside, so what. What is the smallest number of $3\times 3$ that are$3 \times 3\times 3$ cubes needed to fill biggercover the large cube?
The small cubes can overlap. They must be placed at integer coordinates and aligned with the large cube: if you divide the $10\times 10\times10$ cube into $1000$ unit cubes, each $3\times3\times3$ cube should cover $27$ of those unit cubes.
The boundary of the $10\times 10 \times 10$ cube is periodic: if you have a small cube intersecting one face of the large cube, it wraps around to come back in from the opposite face, Pac-Man style. sorry i dont know tex
