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Asteroid walk (Posted on 2016-04-19) Difficulty: 3 of 5

Seven astronauts landed on a small spherical asteroid. They wanted to explore it and walked in different directions starting from the same location. All used the same walking algorithm: walk x kilometers forward, turn 90 degrees left and walk another x kilometers, turn 90 degree left again and walk the last x kilometers. The value of x was different for different astronauts and was one of 30, 40, 50, 60, 70, 80, and 90.

All but one astronaut finished in the same location. What was the value of x for the astronaut who finished alone? What is the size of the asteroid?

(Konstantin Knop)

See The Solution Submitted by broll    
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Question question | Comment 1 of 8
Are we to assume the astronauts walk in the nearest thing to a straight line--that is a great circle path?  Or do they, already knowing the size of the asteroid, make one of the legs of their journey follow a lesser circle, such as a parallel of latitude? The latter would make the situation similar to the polar bear puzzle near the north pole (or maybe a penguin near the south pole)
  Posted by Charlie on 2016-04-19 22:46:24
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