perplexus.info :: Just Math : Gardener's Woe

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

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2024-02-10 22:13:41
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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