Question 71
Given a $10 \times 10 \times 10$ box of $1000$ unit white cubes. An and Binh play a game with this box. An selects some bands of size $1 \times 1 \times 10$ such that any two chosen bands have no common points and then changes all cells on these bands to black. Binh then selects some unit cubes and asks An what color of these cells. What is the least number of cells Binh must choose in order to determine all black cells based on An's answer?