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 Some thinking by Old Original Oskar!)

The thing is, the snail must go to the CLOSEST plant, so the snail would actually go to (1,1) then to (2,2) and so on, and will only take 10 steps. The longest I've got for 5 seedlings is 22 steps, anyone got a larger answer?

Posted by Victor Zapana on 2006-06-24 14:09:25