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Counting Ten Segment Paths (Posted on 2016-02-19) Difficulty: 2 of 5
Multiple paths can be drawn on the grid below following along ten of the twelve segments but never using any segment twice.
+--+--+
|  |  |
+--+--+
|  |  |
+--+--+
How many such paths are there?

No Solution Yet Submitted by Brian Smith    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts As many as I found | Comment 1 of 6
I found 9 ignoring reflections and rotations:
+-a-+-b-+
|c  |d  |f
+-f-+-g-+
|h  |i  |j
+-k-+-l-+

There have to be two unused segments.
The path is only possible if the missing segments are a&c, d&f, or f&g.

Missing f&g: One path:
achkidbfjl

Missing d&f: Three paths:
jlkhcabegi
jligebachk
giljebachk

Missing a&c: Five paths:
gfhkidbejl
ebdfhkigjl
ebdikhfgjl
gfhkljebdi
ifhkljebdg

I wouldn't be surprised if I missed one or two.


  Posted by Jer on 2016-02-19 11:03:32
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