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.

My best effort after creating the problem was less than either Dej Mar's best or Charlie's (almost certainly) optimal.

I was surprised to see the increase of 6 seedlings over 5 was less than 12% since it is much larger for fewer seedlings.

Charlie, would you mind rerunning your program to find the solutions for other numbers of seedlings?  From 2 to as high as you feel like would be fine.

Posted by Jer on 2006-06-26 09:50:11