Question regarding operation of a pulse generator circuit with 3 transistors (exercise 2.3 art of electronics)
When the input pulse is not present the output transistor (Q2) is on hence the output is low. This is because R3 biases it on. When the input pulse arrives Q1 is switched on and this (via C2) takes Q2's base low and turns Q2 off; thus the output then goes high. This also turns on Q3 and Q3 reinforces the action of Q1 switching on. In effect, if Q1 was on for a very short time Q3 would "remember" this and keep both collectors low.

After a while C2 charges to a point where the voltage on the base of Q2 starts to turn Q2 back on. The onset of Q2 turning on is also the onset of Q3 turning off and this rapidly causes Q2 to fully turn off.


  What is the minimum required beta of Q3 to guarantee saturation?


Q3 is saturated if it takes a curent approaching 5 mA because that would drop the full 5 volts across R2. Given that the base of Q3 receives about (5V-0.7V)/21kohm = 205 uA, the beta will need to be about 5 mA/200 uA or 25.


  Assuming Q1 is off, does that mean there will be 5+0.94= 5.94mA
  flowing through Q3?


Initially the current will be determined by R1||R3 = 909 ohms and this forces a current of 5/909 = 5.5 mA. As C2 charges this tends to become more like 5 mA.