I'm interested in any information on route 13c, the most challenging one. I planned originally to take the cogwheel train up because I read it was more fun, and hike down. Now I'm thinking it might be better to hike up the hard way and take the cable car down.
I have not hikedonnPalitus but tried (unsuccessfully) to find a map that showed a route 13c. This is the map I did find:
It shows a trail up to the Kulm from Alpnachstad which takes 4.5 to 5 hours and is rated "moderate to challenging" ( 3 hikers).
And a trail up from Kriens via Fräkmüntegg which takes 5.5 hours and is rated "challenging" (4 hikers).
Which one is the one you are considering, and what is the question you are asking?
I would always check for hiking maps and advice at the local tourist information office. In Switzerland, they're particularly helpful.