(B) Under what circumstances would removal of two squares from an 8x8 chessboard allow such a tiling? For example, if we remove an arbitrary white square and an arbitrary black square, can the remaining board be tiled?
(C) A hospital has 16 isolation rooms. Patient 13 is cured. He wants to pass by all other patients before leaving but he can't see the same patient twice or he will get sick again. Is that possible?
[Also known as 'Patient in Room 13 Puzzle' or 'Quarantine Puzzle'; it surfaced in 2020 after Covid-19 caught us by surprise.]
(D) In the above puzzle, imagine that we have a helicopter in one of the squares to bail us out of the hospital (instead of a door as suggested by the red arrow above). Is there a room such that if the helicopter were in that room, the puzzle would be impossible to solve?