> I looked up all the hints that I could find, drew the diagram, and plotted out, what looks like it would work, but when I used it, it didn't! I've double checked everything, actually, I've quadruple checked everything. Here's the combination I have:
>
> To go from 01W-01E-06E-06W-11W-11E-16E-16W-21W-21E-26E-26W-01W
>
> (N-North, S-South, O-Outer, I-Inner)
> 01W:N,O
> 01E:O,S
> 06E:N,O
> 06W:O,S
> 11W:N,I
> 11E:I,S
> 16E:N,O
> 16W:O,S
> 21W:N,I
> 21E:I,S
> 26E:N,O
> 26W:O,S

Your path crosses the outer parallel three times in a row, going through medians 26, 01, and 06 toward the south. You're almost there; just remember that one rule was it needs to alternate crossing the inner/outer.