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.
The two points
(0,0) (9,9)
Give a total distance of 12.72792206135786
The three points
(0,0) (9,0) (1,9)
Give a total distance of 21.0415945787923
The four points
(0,0) (7,5) (9,0) (0,9)
Give a total distance of 26.71541213553499
The five points
(0,0) (6,5) (9,9) (9,0) (0,8)
Give a total distance of 33.85184425469895
The six points
(0,0) (6,5) (5,9) (9,9) (9,0) (0,8)
Give a total distance of 36.97494988031661
The seven points
(0,0) (7,3) (8,6) (5,6) (9,9) (9,0) (0,8)
Give a total distance of 39.8196453448246
Puzzle Answer
