With a continuously running clock do one pull-up the first minute, two pull-ups the second minute, three pull-ups the third minute... continuing as long as you are able.
Use as many sets each minute as needed.Ken and I ended up doing one complete series on the bar then after a 15 minute rest, did a complete series on the rings.
Bar: 14 Rounds + 13 reps = 118 pullups
Rings: 11 Rounds + 10 reps = 76 pullups
Grand Total = 194 pullups