There 24 hours in a day. If her doctor told her to take a pill every 6 hours, technically, she needs to take 4 pills in a day (since 6 X 4 = 24 which is the number of hours in a day). After 24 hours, there will only be 13 pills left. After 48 hours, there will be 9 pills left. That goes on. So the pills will only last for 4 days and will only be able to take 1 pill on the 5th day.
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