Santa Delivers Presents
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 \(10\) degrees, and travels the great circle, ending up back at the North Pole. He repeats this until he traveled through all the great circles \(10\) degrees apart. If he has to do all of this in \(12\) hours, then the smallest possible integer average speed in km/h for him to make it is \(N\). Find the last three digits of \(N\).
Assume that the Earth is a perfectly spherical \(12,742\) km diameter ball.