🤔 clock math puzzle
- how much time passes between each time the minute and hour hand overlap?
- method 1:
- notice that over a 12 hour period, it will happen only 11 times
12 hours / 11 occurences * 60 minutes / 1 hour=> 65.45 minutes / occurence=> 1 hour 5 minutes and 27 seconds / occurence
- method 2:
t = minutes since noonm_deg = minute hand degrees = 360 * mod(t, 60) / 60h_deg = hour hand degrees = 360 * t / 60 / 12- ie. when does
m_deg = h_deg360 * mod(t,60) / 60 = 360 * t / 60 / 12mod(t,60) = t / 12t - 60 N = t / 12 (where N is an integer)t = N 12 * 60 / 11 (where N is an integer)- (same as method 1)