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.

Starting from 0,0 and going to 7,7 then 10,10. Now the slug has 2 possibilities to go either 0,10 or 10,0 and after choosing from those it crosses the field to get to either 0,10 or 10,0. Either way the distance would be 10(1+2√2) which is about 38,28 units

Posted by atheron on 2006-06-25 10:54:47