# The traveler first walked 50 km to the north, then turned and walked 60 km to the west, turned again and walked 50 km

The traveler first walked 50 km to the north, then turned and walked 60 km to the west, turned again and walked 50 km to the south and ended up at the starting point of the path Where could he be at the beginning of his journey? Is there one possibility of such a movement?

1) The traveler could be at the South Pole of the Earth. Then he could walk 50 km in any direction from it to the north, then 60 km strictly to the west (in a circle centered at the pole) and again south to the pole.
2) The traveler could also be 50 km from the points of the Earth, distant from the North Pole at a certain distance R, so that the circle centered at the North Pole is a multiple of 60 km. That is, the traveler walked 50 km towards the North Pole, and then walked around it (once, if the circumference is 60 km, twice, if the circumference is 30, etc.) and then went 50 km south – to starting point. It is clear that such possibilities are endless.

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