This is taken from "Undestanding Analysis"- Abbot,
Exercise 4.5.8: Imagine a clock where the hour hand and the minute hand are indistinguishable from each other. Assuming the hands move continuously around the face of the clock, and assuming their positions can be measured with perfect accuracy, is it always possible to determine the time?
From my point of view, I think we CAN tell the time because if you observe for, say, 5 minutes, you can see that the minute hand moves faster than the hour hand. Having that, you can determine which one is the hour hand and which one is the minute hand, and hence, you can easily deduct the exact time. However, this is not very mathematical, and although there is a solution for this question, I do not want to look at it so it would be better that I come up with my own original solution.
So, please help me, did I answer this question correctly? How do I move up my argument to a solid proof statement? I thank you very much for your help.