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It depends on how you define "daylight". If you mean, "For how much time does the Sun shine on the north poles?", then the answer would be that the Sun shines for just as long on the North Pole as it does anywhere else on Earth, exactly 6 months. The difference is that the North Pole gets the sunlight in one long day while most of the rest of the Earth divides the time up among the 365 days of the year. On the other hand, if you mean, "How much energy does the North Pole receive from the Sun?", then the answer is much more complicated. The total amount of energy is dependent on how high the sun is above the horizon. At the North Pole, the Sun's angle above the horizon ranges from 0° (on the horizon) on the equinoxes and 23.5° at the June solstice. This low angle means that the Sun's energy is very spread out on the surface. Thus, it never gets very warm at the pole. However, I am not sure how to calculate just how much energy is actually received during the pole's day.
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