mathematics - Consecutive numbers that are Manhattan distance 3 apart

Can you place numbers from 1 to 16 on a 4x4 grid, such that the distance between any two consecutive numbers ($a$ and $a+1$) is Manhattan distance 3?

Bonus question: can you also make 1 and 16 be separated by Manhattan distance 3, thus making it a closed tour?

Note that the Manhattan distance between two locations is the distance between their row locations plus the distance between their column locations.

Good luck!

Answer

I think this works.

Method:

It can't just be a knight's tour, since they don't exist on 4x4 boards. So I figured I would get to a corner and just knock out all four corners in a row. The rest was trial and error, except in this case I didn't happen to hit any errors.

Oh, I don't think the bonus question was in there when I was solving this. I can take a look later. Here we go:

Method:

I just backtracked from the original solution; I had to back up to the 10 and try a couple paths but it was pretty straightforward.