Answer this question without Google (Creative thinkers enter)

[Fry]

@cdvma

I didn’t read all of your answers but this one stuck out. This doesn’t work. By this then you say the hands line up at 6:30 and that is not the case (its the easiest negative proof to visualize) since the hour hand will be half way between 6 and 7 but the minute hand is dead on 6.

The quick and the dirty is the minute hand always rests at the same places every rotation so its position can be described as Y=(360/60)X where X is the time in minutes (or partial minutes) and Y is the angle in degrees. The hour depends on what hour it is currently so its a bit different: Y=(30HOUR)+(30*(MINUTE/60)). Set those two equations equal to eachother and you can solve for which minute and hour by fixing hour and solving for minutes.

Charting this you can see the minute angle line intersect 12 individual hour angle lines (each have the same slope but are offset 30* on the x axis).

Since the minute angle slope is constant and the hour angle is just offset by the same with each additional hour it is a fixed difference. Its just not 5 minutes

Of course there is also the simple explanation that there are 10 unique , individually spaced intersections on the dial not counting the zero position. 60 minutes with 10 divisions is 6 minutes each

Goddammit 24 times you fuck. The minute hand passes the hour hand, momentarily lining up, every hour.