Today you saw two infinitely long buses with seats numbered as \(1,2,3,...\) carrying infinitely many guests each arriving at the full hotel. How do you accommodate everyone?
In a distant village of \(3\) houses all villagers want to have access to all \(3\) wells. Is it possible to build non-intersecting straight paths from each house to each well?
In good conditions bacteria in a Petri cup spreads quite fast, it doubles every second. If, initially there was one bacteria, then in \(32\) seconds they will cover the whole surface of the cup. In what time the bacteria will cover the surface of the cup, if initially there were \(4\) bacteria?
Find the area of the largest piece cut out from a regular chessboard, which contains exactly \(4\) black cells. You are only allowed to cut along the edges of the cells and the piece must be connected, namely you cannot have cells, attached only with a vertex, there has to be a common edge.