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Puzzle Details

I was having trouble sleeping last night and I tossed and turned well into the night.

Our local town hall has a clock which strikes on the hour and also strikes just once on the half hour.

During one of my more awake moments I heard the clock strike once, but I could not tell what time it was.

Half an hour later it struck once again, but I still could not tell what time it was.

Finally, half an hour later it struck once again and I knew what the time was.

What time was it?

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Hint: When does the clock strike just once?

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