You just got a new clock, but it's broken. Your friend tells you he can fix it, but he needs a little bit of data from it. One thing he needs is how many times 1 appears in the run of 2 days.
The rules of this broken clock:
This is a digital, 12 hour display (AM/PM) clock
Every second hour it is blank (odd-valued hours of both days)
Every third hour the digits behind ':' are blank (2, 5, 8, and 11 AM and PM of both days)
Every fifth hour the digits after the ':' are blank (4AM, 9AM, 2PM, 7PM of day 1, then 12AM, 5AM, 10AM, 3PM, 8PM of day 2)
Every time the digits after ':' are a multiple of both 3 and 4, the digit after ':' is blank
If the clock runs for 2 days (starting at 12:00 AM), how many times will '1' appear? Appearances reoccur every minute; thus 12:07 and 12:08 contribute two separate appearances, despite the 1 being displayed constantly.