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.

I have not tested out all the likely possibilities yet, but to offer a start....

The slug beginning at (0,0) goes to the next seedling that sprouted at (4,6) which is a distance of 2*SQRT(13) [approx. 7.2111] away. Then the slug travels 5 units to (0,9). After consuming that snack, the slug travels to the doomed seedling at the corner location (9,9) at a distance of 9, and finally to consume the seedling at (0,8), a distance of SQRT(82) [approx. 9.0554].  Thus, for 5 seedlings  the slug would travel approximately 30.2665 units.

Posted by Dej Mar on 2006-06-24 15:30:20