From the 7th October till the 4th Mar, there is 24 hour a day darkness at North Pole.
From the 18th March till the 24th September, there is 24 hour a day daylight at the North pole.
But between the 5th -17th March, and then again, from 25th Sep to 6th October, you get 24 hour a day twilight at the North Pole, ie, the Sun is permanently below the horizon, but never lower than 6º depression angle.