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 My solution for 6 seeds by atheron)

The word "array" implies that each doomed seed was planted in a seperate unit square "lot".  Given the array is 10x10 and that the southwest corner is assigned (0,0), the northeast corner would be assigned (9,9). 

Though Jer did not indicate that these seeds were planted in the center of each "lot", I believe the assumption can be made that they were.  As you even made the assumption to use only interger points in your solution. 

Edited on June 25, 2006, 8:13 pm

Posted by Dej Mar on 2006-06-25 20:11:59