Four ships are sailing on a 2D planet. Each ships traverses a straight line at constant speed. No two ships are traveling parallel to each other. Their journeys started at some time in the distant past. Sometimes, a pair of ships collides. A ship continues its journey even after a collision. However, it is strong enough only to survive two collisions; it dies when it collides a third time. The situation is grim. Five of six possible collisions have already taken place (no collision involved more than 2 ships) and two ships are out of commission. What fate awaits the remaining two?

This puzzle is obtained from https://gurmeet.net/puzzles/four-ships/index.html

I found a similar question online Ghost Ship Collisions but this visualises a tetrahedron and thus says that the ships won't collide further but I cannot think of any 3D figure smaller than tetrahedron that has 4 edges, thus I am stuck.

  • $\begingroup$ Note: a tetrahedron has four faces but six edges. In any case, if you're thinking in terms of constructing a surface with finite area but no boundary then there there are innumerable ways to do it. For example, if you imagine taking a rectangle and connecting the top and bottom edges to each other, and the left and right edges to each other then, in the simplest case, your surface is equivalent to that of a torus. On the other hand, note also that that tetrahedra and toruses are 3D figures, not 2D. $\endgroup$ Aug 13, 2023 at 14:34

1 Answer 1


I think the fates could turn out to be good and bad both, assuming that the ships are sailing with constant speed, but not every ship is having exactly the same speed:


Note: If there was not a starting point in the past, both surviving ships were already collided with each other.




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