# 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 $$10$$ 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.

×