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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.
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How many such paths are there?

No Solution Yet Submitted by Brian Smith    
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Solution Missed a few before--now added; As well as I can classify them | Comment 5 of 6 |
(In reply to re(2): As many as I found by Charlie)

I neglected those starting with a spoke; those starting with segment f are now included as well as those already reported starting with segment h. Although there are 34, there are in fact some reflections, as for example f followed by i is a reflection of f followed by d:

hkifcadgjl  be
hkifcadgeb  jl
hkifcabegd  jl
hkifcabejl  dg
hkidacfgjl  be
hkidacfgeb  jl
hkidbegfca  jl
hkigebacfd  jl
hkigebdfca  jl
hkljgfcadi  be
hkljgfcabe  di
hkljgdacfi  be
hkljebacfi  dg
hkljebacfd  gi
hkljebacfg  di
hkljebdfca  gi
fikhcadgjl  be
fikhcadgeb  jl
fikhcabegd  jl
fikhcabejl  dg
filjgdachk  be
filjebachk  dg
fdachkigjl  be
fdachkigeb  jl
fdachkljgi  be
fdachkljeb  gi
fdbegikhca  jl
fdbejlkhca  gi
fgjlkhcadi  be
fgjlkhcabe  di
fgjlidachk  be
fgebachkid  jl
fgebachklj  di
fgebdikhca  jl

but it's still true that with rotations and reflections counted separately the total is 200.

  Posted by Charlie on 2016-02-19 14:59:11
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