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OK, the solenoid has a long power stroke because the piston has a magnetic pole which is always inside the coil.It is not usually possible to make a magnet with three poles but that is in effect what I did. If you place two magnets with like poles adjacent they will repel, if you place them on the ends of a short bar with like poles towards the ends of the bar they will be repelled. But if the bar is long enough they will stick to the bar and if you check with a compass needle you will find there are is a single strong pole induced in the middle of the bar, actually it is two like poles very close together but for our purpose we can consider them a single pole.