Owl A,B,C

Owl a gives a hoot every 7 minutes. Owl b gives a hoot every 9 minutes. Owl c gives a hoot every 5 minutes except when he has heard owl a or b give a hoot within the previous 2.5 minutes. If this happens, owl c doesn't give a hoot. If all three owls give a hoot at the stroke of midnight, how many times after midnight and before 1:00 am does the owl c give a hoot?

Final Answer:

n =  5

Step-by-step explanation:

$$\begin{gathered} t=1\text{h}\to \text{min}=1\cdot 60\text{min}=60\text{min} \\ a:7,14,21,28,35,42,49,56 \\ b:9,18,27,36,45,54 \\ c:5,10,15,20,25,30,35,40,45,50,55 \\ {c}_1:5,25,35,40,45 \\ n=5 \end{gathered}$$

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