Santa Delivers Presents

Geometry Level 4

Santa wants to deliver presents to every little boy and girl in the whole world. He plans his trip as follows: starting from the North Pole, he travels along a great circle cutting through both poles, ending up back on the North Pole. Next, he turns his path by 1010 degrees, and travels the great circle, ending up back at the North Pole. He repeats this until he traveled through all the great circles 1010 degrees apart. If he has to do all of this in 1212 hours, then the smallest possible integer average speed in km/h for him to make it is NN. Find the last three digits of NN.

Assume that the Earth is a perfectly spherical 12,74212,742 km diameter ball.

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