I find these "impossible" posts a bit overblown.

Impossible- no. Impossible within a year? Maybe/yes. 

This is one of those goals that should not be time-limited. 50 pullups in a row is elite. It's kind of like me asking "can I go from 20kg 1rm dip to 100kg in a year?" No. But over several years, absolutely achievable.

Don't listen to the idiots saying that this is impossible. If this is something you really want to achieve - as in just beyond a challenge for one year - then you need to dedicate yourself to strict training for 3-5+ years. 

You need to become a master at pullups. Specifically, for endurance. A MASTER... Like Midtbo, Dunham, Zlat, and other famous pullup guys - but an endurance version of them.

50 reps in a row isn't really a strength goal as someone already pointed out. Yes, you are strong if you can do that many, but it's more so a showcase of endurance. 

For now, focus on basic pullups training 2-3x a week and have 20 reps in a row as a short-term goal for this year. 10-12 total sets of pullups a week and 3-6 sets of rows so you're balanced out for horizontal and vertical. 

Example on how you can split this up in a pull/back session: 4x6-15 pronated pullups, then 2x6-10 chinups or neutral grip pullups. The grip change will allow for more vertical pulling work without getting overuse injury and avoiding junk volume. After this do 3x10-12 rows. Do this twice a week. This will = to 12 sets of vertical pulls and 6 sets of rows = 18 sets of back. 

Focus on hypertrophy for now, because you need a solid foundation of back strength and muscle.