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 Gardener's Woe (Posted on 2006-06-24)
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.

 Submitted by Jer Rating: 4.0000 (1 votes) Solution: (Hide) 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 Thanks to Charlie for finding 5, 6 & 7

 Subject Author Date re(3): Nicely done -- now through 7 seedlings Jer 2006-06-26 18:58:23 re(2): Nicely done -- now through 7 seedlings Charlie 2006-06-26 13:47:48 re: Nicely done -- 2 thru 6 seedlings Charlie 2006-06-26 11:15:09 Nicely done Jer 2006-06-26 09:50:11 re(2): computer solution to 6 Charlie 2006-06-26 09:48:59 re: My solution for 6 seeds Dej Mar 2006-06-25 20:11:59 re: My solution for 6 seeds Charlie 2006-06-25 20:02:02 My solution for 6 seeds atheron 2006-06-25 19:03:09 re: computer solution to 6 Dej Mar 2006-06-25 17:11:57 computer solution to 6 Charlie 2006-06-25 16:13:48 computer solution for 5 Charlie 2006-06-25 15:07:10 re(2): My solution for 5 seeds atheron 2006-06-25 14:23:07 re: My solution for 5 seeds Jer 2006-06-25 11:26:50 My solution for 5 seeds atheron 2006-06-25 10:54:47 Slimy trails (6 seedlings spoiler?) Dej Mar 2006-06-25 09:12:21 re: The long dusty trail of slime (5 seedlings spoiler) brianjn 2006-06-25 00:40:27 The long dusty trail of slime (5 seedlings spoiler) Dej Mar 2006-06-25 00:11:30 'Arcs' for part 2 brianjn 2006-06-24 21:54:21 'Arcs' for part 1 brianjn 2006-06-24 20:46:15 re: Clarifications and stuff (spoiler) Dej Mar 2006-06-24 19:45:50 Clarifications and stuff Jer 2006-06-24 17:01:57 did I understood correctly? atheron 2006-06-24 15:42:00 possible solution for 5 seedlings (spoiler) Dej Mar 2006-06-24 15:30:20 re(2): Some thinking Federico Kereki 2006-06-24 14:45:52 re: Some thinking Victor Zapana 2006-06-24 14:09:25 Some thinking Old Original Oskar! 2006-06-24 12:50:04

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