I happened to see this puzzle on Facebook. Really nice puzzle (if rather hard).
Seven astronauts are exploring a small spherical asteroid. All seven started out in the same point.
Astronaut A went 30 kilometers in one direction, then turned 90 degrees to the left, then moved another 30 kilometers, then turned 90 degrees to the left again, and then moved for 30 kilometers more.
Astronaut B moved in the same pattern, except his movements between the 90 degree turns were 40 kilometers long instead of 30.
Astronauts C, D, E, F and G also moved in the same pattern, but went in sections of 50, 60, 70, 80, and 90 kilometers, respectively.
The astronauts started moving (from the same starting point) in several different directions, but, as it happened, after the movements described above, all but one ended up in the same place.
- Which astronaut ended up in a different place?
- How large is the asteroid?
Answers in comments (if there somehow are any).
(Post 172 in the inner system, incidentally. Post 4 in reality.)