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 Clarifications and stuff by Jer)

A slime trail of (0,0)...(4,8)...(0,9)...(9,9)...(9,0) is approximately 31.06737754 units in length.  This might be the longest for 5 seedlings.

Edited on June 24, 2006, 11:00 pm

Posted by Dej Mar on 2006-06-24 19:45:50