In Gardener's Woe http://perplexus.info/show.php?pid=4770 the seedlings could only come up at integral locations. Now let's allow for the seedlings to be anywhere within a unit square:
A gardener has broadcast seeded a 1 meter plot and only some of the seeds sprouted. A hungry slug is eating the first seedling, which is at position (0,0). When it is finished it will go directly to the next closest* seedling and so on until all have been consumed. Where are the seedlings located if the total distance travelled is maximized?
Solve for 2,3,4,5,6 etc. seedlings inside the square garden?
*An important change needs to be made from the original version:
The slug may now have to choose between equidistant seedlings. In any situation where it would have to choose, you may choose the desired path for it.
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