Cup 3. In fact cup 1 and 3 would be the only ones to get any water in them at all (cup 1 would be half full, cup 3 would be full, and cup 2/4/5/6/7 would be completely dry). The spout into cup 3 is lower then the spout into cup 2 and due to this no water would even reach the spout to cup 2 and it would all be forced to the lower spout towards cup 3. Once in cup 3 it would stay there and slowly fill the cup since the spout to cup 4 doesn't actually have an opening, and neither does the spout to cup 5.
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Unless the whole room fills up.