Four ships

Four ships are sailing on a 2D planet. Each ships [sic] 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?

Solution to metapuzzle: show

There's a serious issue with the problem statement: what is a "2D planet"?

I grew up in England at a time when the currency was pounds, shillings, and pence. So for me, "2d" means two pence, pronounced "tuppence". My first thought was that a "2D planet" is a tuppeny planet, what Americans might call a 2¢ planet or a two-bit planet: an almost worthless planet. No, that thought isn't going anywhere useful.

Ok, we live on a three-dimensional planet, a 3D planet, a ball. So a 2D planet must be a disk, with ships sailing along its surface, which is a circle. As they've no scope to pass each other, each pair will inevitably collide, multiple times while they survive. That doesn't provide an interesting puzzle.

But in the course of thinking about it, I drew a diagram of what the ships' courses might look like, with the horizontal axis showing distance around the circle, and the vertical axis showing time.

Then I realised that if I took my diagram, regarded the two axes as two spaces dimensions, and then tilted it into a third, time, dimension, I would have a 3-domensional diagram showing the courses of four colliding ships traversing a flat ocean. So "2D planet" could be a really weird way of specifying "plane", and my diagram would be a proof that the remaining two ships were due to collide!

So, by pursuing my obviously mistaken of "2D planet" as "circle", I had stumbled on the setter's apparent meaning "plane", along with the solution.

Restated puzzle: show

Four ships are sailing on an infinite plane ocean. Each ship 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?

Solution to puzzle: show

Comments: show

I really liked this puzzle.

I think that divining the setter's intention simply by trying to understand the problem statement as worded is impossible. But by working on a clearly wrong interpretation, I stumbled upon a solution that could be modified to apply to what I then realised must be the setter's intended puzzle.

So I could not solve the puzzle without solving the metapuzzle, and I could not solve the metapuzzle without trying to solve a misinterpretation of the puzzle statement. I solved the metapuzzle and the puzzle simultaneously. I found that very pleasing.

I'm confident that this metapuzzle-puzzle pair was not the setter's intention. "2D planet" is just a really naff way of specifying "plane", "infinite plane", or "Euclidean plane".

Four colliding ships

Problem statement

Solution to metapuzzle: show

Restated puzzle: show

Solution to puzzle: show

Comments: show