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.

By using integer points I'm able to come up with over 40 units.. Start from 0,0 then to 7,7 -> 10,6 -> 10,10 -> 10,1 -> 0,10. This way the distance will be 7√2+√10+4+10+√181 which is appr. 40,51 units!

Posted by atheron on 2006-06-25 19:03:09