An unlucky gardener planted a 10x10 square array of 100 old seeds out in the garden. Only 5 of these seeds have germinated including one at the southwest corner (0,0) where a slug is currently reducing it to ground level.

When it finishes it will head directly to the next closest doomed plant. After it eats that one it will again leave a slime trail to the closest remaining plant and so on until the garden is no more.

Where are the 4 remaining seedlings if the path crawled by the slug is the longest possible and it never has to choose between two equidistant snacks?

Note: Although the slug will never have to choose between two equidistant seedlings, this doesn't imply that no two are equidistant.

Next find the locations if 6 seedlings had germinated instead of 5.

(In reply to Nicely done by Jer)

The results for 2 thru 6 seedlings are:

0  0     9  9     12.72792206135786
0  0     9  0     1  9     21.0415945787923
0  0     7  5     9  0     0  9     26.71541213553499
0  0     6  5     9  9     9  0     0  8     33.85184425469895
0  0     6  5     5  9     9  9     9  0     0  8     36.97494988031661

Things get slow enough for 6 seedlings, so I'll try converting to Visual Basic for larger numbers of seedlings.

Posted by Charlie on 2006-06-26 11:15:09