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Scarab Sages

I am DMing a campaign for the first time (and playing for the first time consequently) and we are a bit confused on the whole "per day" concept of spell limits. If my player's Sorcerer can cast 4 level one spells per day, is that per 24 hour cycle or every time he gets 8 hours of rest + 15 minutes to prepare his daily spells?

In other words:

A) Can the sorcerer blow all his spells on an encounter and then rest for 8 hours and bam, they are all ready again? Can he do this over and over again? Theoretically 2-3 times every 24 hour cycle?

B) He blows through all 4 of his spells in an encounter. He then must get at least 8 hours of rest in the next 24 hours but can't cast them again regardless until at least 24 hours have passed?

C) Is the "day" cycle 24 hours from, say: 12:01 a.m. Monday to 12:01 a.m. Tuesday and between those hours the Sorcerer must get at least 8 hours of rest.

Any input would be much appreciated.