How to find the hour and minute for the times when the hour and minute needles will be exactly over each other?

First of all let us analyze the problem. The hour hand moves 30 degrees for a 360 degree movement of the minute hand. Therefore if the hour hand is currently at h angle then the minute will be at 12*h angle. The other thing is that beyond 360 we have to get back between 0 and 360 therefore we will take the modulus.

Here is the Python code for finding this out.

hour=0

interval=0.1

a=[]

print("Hour angle =",0,", Minute angle ",0,", Hour=",0,", Minute=",0)

prevhour=0

prevminute=0

prevdifference=0

hour=interval

while hour<360:

    minute=12*hour

    minute=minute%360

    minute=round(minute,3)

    hour=round(hour,3)

    difference=hour-minute

    difference=round(difference,3)

    if prevdifference>0 and difference<0:

        print("Hour angle =",hour,", Minute angle ",minute,", Hour=",hour//30,", Minute=",round(minute/6,3))

    prevhour=hour

    prevminute=minute

    prevdifference=difference

    hour=hour+interval

The output