This is a great day hike. In my opinion the best way to solo hike Mt. Washington. It only requires one car and you can spend a night in a hotel. The trail starts in the parking lot for the Cog Railway, its name is Ammonoosuc Ravine Trail. I dont have the exact mileage but the trip up is pretty steep. The Ammonoosuc river comes right off the side of the mountain and the trail switch-backs up the ravine. Its pretty cool, like walking next to a water fall. The trail will connect you to the Crawford Path/AT at Lake of the Clouds.
The Crawford Path will then take you to the summit. Hopefully it's a nice day and you can spend plenty of time at the top. On the way down you should take the AT/Gulfside Trail. If you have time I would go to the top of Clay, a small mountain in comparison but with a nice view.
The Jewell Trail is right before the Mt. Clay Summit Trail. This will take you down to the Cog Railroad parking lot. Its a nice loop and is difficult at the same time.
If you want you could always take a one way ride on the railroad which would cut the trip time in half.
Take Rt. 302 North until you reach Base Station Road which will take you to the Cog Railway station.
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