What serial number is referred to in a cq contest? How do I determine that serial number?
Serial numbers usually count from 1 to N where 1 is for your first contact of the contest. Serial numbers are incremented by 1 typically. But, there is no reason why you cannot start at 577 and increment by 5 if you want unless the rules require you do count in a specific fashion [Recently added update per discussion in comments].
I actually start at 22 for some reason. All my contests I do are CW and I just like the sound of 22 I guess.
Also, during a contest when the exchange uses serial numbers, the other operator will give you his serial number and you give yours. Of course the numbers are not the same. In contesting and submitting your log, serial numbers are usually included to demonstrate a qualified contact.