A cube with size 10 * 10 * 10 consists of 1000 unit cubes, all colored white. A and B play a game on this cube. A chooses some pillars with size 1 * 10 * 10 such that no two pillars share a vertex or side, and turns all chosen unit cubes to black. B is allowed to choose some unit cubes and ask A their colors. How many unit cubes, at least, that B need to choose so that for any answer from A, B can always determine the black unit cubes?
Thanks! I read the word "pillars" and mistakenly thought 1*1*10 instead of what was printed: 1*10*10.
Here is a quibble then with the "13" solution. If we are looking for a single pillar, checking 9 of the 10 on the diagonal would suffice, as 9 white infers the 10th to be black.
smoke clears
