​Why stop at one broken clock?

Y’all know the saying that a broken clock is right twice a day, well it got me thinking that if you have enough broken clocks around you you can always know what time it is. My first thought was that you would need 180 clocks, but later reflection told me that this would only get you accuracy to every 4 minutes. To get accuracy to the minute you would need 720 broken clocks. Of course this creates the problem of which clock is the right broken clock to observe. But I have a solution! Mount all 720 broken clocks on a mechanically rotating wheel so that the correct clock is always showing through a hole in a screen of some sort! This way we can repurpose all of the broken clocks and make a simpler time piece!