Consider a clock with an hour hand and a minute hand. Starting from midnight, how many times do the hands cross each other in 24 hours.
Note, you don't count the starting point of midnight, with the hands overlapping as a crossing, but you do count the last moment, when the two hands overlap at midnight a day later.
Bonus Question:
Normally, clock hands travel clockwise around the clockface. Suppose now that the two hands are travelling in opposite directions. How many times do the hands cross in this case?
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