For a project, a few computer science students form a virtual planet called SRAM. They introduce a new calendar and time period structure where there are 8 days per week, starting Sunday to Saturday and another day called Funday. Every day is of 36 hours and each hour is of 90 minutes. Each minute is of 60 seconds. Hour hand covers the dial twice daily. What is the angle between the hour and minute hand when time is 12.18 am?

Using the variable clock angle formula, we first find the angle of the minute hand at 18 minutes: (18 / 90) * 360 equals 72 degrees. We then calculate the hour hand angle, noting that in an 18-hour half-cycle (from 12 to 6), 18 minutes constitutes 1.8% of the cycle, yielding a position of 6.48 degrees from the top. Finally, by adding the 72 degrees of the minute hand movement to the 93.6 degrees traversed by the hour hand over 18 minutes, we find the hands are 172 degrees apart.

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