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.

Because of symmetry, I think he must have remained in the main diagonal. I would bet on his path going from 0,0 to 9,9 to 1,1 to 8,8 to 2,2... though maybe 0,0 to 8,8 to 1,1 to 9,9 to 2,2 is longer; will do the numbers! (Just a feeling that maybe you get the maximum when all steps are as similar as possible.)

Posted by Old Original Oskar! on 2006-06-24 12:50:04