The quick and easy guide to 20 deadhang pull-ups

For my conditioning today I warmed up with a little drill I used to do every morning and evening about two summers ago. This was the trick that allowed me to knock out 20-25 deadhangs and 60-75 push-ups so long as I had a day's rest before, and often even without that. This was in addition to at least one workout and often two daily, usually the CrossFit WOD plus running or heavy lifting two or three times a week.
Basically, the idea is you do deadhang pull-ups to Pavel's "comfortable stop" and immediately drop and do push-ups. The number of push-ups to do is calculated by multiplying the number of pull-ups by 2.5. Immediately upon finishing the push-ups, you get back on the bar and do pull-ups so that the total of the 2 sets of pull-ups is 20, and then do push-ups so that the total of the two sets is 50.
Rest between sets should be kept at a minimum. At most maybe a few quick breaths and a few seconds of shaking out the limbs should suffice. The goal here is to accomplish the work fairly quickly, so that even a second set of 3 pull-ups feels hard.
When you get to the point where you can get 20 pull-ups and 50 push-ups fairly routinely, bump the pull-ups up by 5 and the multiplier up by .5. Now you will be doing 25 deadhangs and 75 push-ups in two sets per exercise.
An example session might look like this:
Set one: 15 pull-ups followed by 38 push-ups
Set two: 5 pull-ups followed by 12 push-ups
As you can see, in this example the athlete would have to decide how to split up the push-ups, since 15 times 2.5 is 37.5. Basically it's not important at all how one decides to split this up as long as the total of the two sets of push-ups is 50. This is because being able to do a lot of push-ups was not a goal of mine when I designed this program.
If you have a goal of doing a lot of pull-ups there are a lot of programs out there. I have had good luck in the past with Grease the Groove, density training, weighted pull-ups etc. The main advantage to this program was that it allowed me to train as fresh as possible as often as possible while practicing conditions that closely mimic the test I wanted to perform. When I tested for 20 pull-ups, I was already used to struggling through the last 5 or so reps, so there was no mental barrier that made me want to drop off the bar before I was truly "done."
I hope this program helps you achieve your goals as it helped me achieve mine.