Question 6
A $10\times10\times10$ cube consists of 1000 white unit cubes. An and Bình play a game. An chooses some $1\times1\times10$ rods so that no two chosen rods have a common vertex or edge, and colours all their unit cubes black. Bình chooses some unit cubes and asks An their colours. What is the smallest number of cubes Bình must choose so that, whatever An's answers, Bình can always determine exactly which cubes are black?
Interpretation: the rods are full axis-parallel rows of the grid, and Bình chooses the whole set of queried cubes before receiving the answers, as in the source solution. “Unit squares” in the printed three-dimensional statement is read as unit cubes.
Interpretation: the rods are full axis-parallel rows of the grid, and Bình chooses the whole set of queried cubes before receiving the answers, as in the source solution. “Unit squares” in the printed three-dimensional statement is read as unit cubes.