Answer: You can turn a square manhole cover sideways and drop it down the diagonal of the manhole. You cannot drop a round manhole cover down the manhole. Therefore, round manhole covers are safer and more practical than square ones.
Answer: There is a complicated way counting a sequence. Or simply knowing that if the fly is flying the 2 hours still at the same speed of 75 km/h then it flies a distance of 150 km.
Answer: You can put one foot-bridge over one corner (thus a triangle is created). Then from the middle of this foot-bridge lay another foot-bridge to the edge (corner) of the castle. You can make a few easy equations confirming that this is enough.
Answer: When the trains encounter, they will be approximately the same distance away from New York. The New York train will be closer to New York by approximately one train length because they’re coming from different directions. That is, unless you take “meet” to mean “perfectly overlap”.