When knowing the way magnets act with each other when in close proximity, you can determine many ways other objects act around them. First, if a magnet runs north to south with the north side of the magnet on the left side of a picture and a compass above the magnet, your able to determine the direction of the compass. Since compass's point in the direction of the magnet field line and the magnets' magnetic field lines run from north to south, the compass would be pointing to the right, since it was above the magnet. Also, a magnetic field strength is greatest when in the most dense area of magnetic field lines. Lastly, the greatest strength of an electromagnet is if it's wrapped in iron. Overall, there's many problems you can solve with magnets, knowing how they act alone and around other magnets.