Time

Puzzle:

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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Solution:

1.30 in the morning. The initial single strike was at 12.30.