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I just had this question in a maths competition. I came to 132 as an answer but I wasn't able to formally show that the answer is correct. Can anyone solve this following problem formally?

Suppose there is a clock that has its minute and hour hands the same length. In a 12 hour period, how many times is the time ambiguous? (when one cannot tell which is the hour/minute hand)

Maths explorer
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    See this. – lulu Sep 04 '20 at 13:12
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    For a very similar problem, see https://mathhothouse.me/2015/08/30/interchanging-the-hands-of-a-lock/ . The legend says that this was the problem posed to noone else but Albert Einstein, once he was ill in hospital, by his friend and biographer, Moszkowski, to kill time. Apparently unsuccessfully, as it took Einstein less time to solve the problem than his friend to state it. The answer $132$ is correct here - from $143$ positions where the hands can be swapped one can subtract $11$ unambiguous ones where hands overlap. –  Sep 04 '20 at 13:12
  • Also, the "Einstein's version" of the problem features on MSE before: https://math.stackexchange.com/q/400425/700480 –  Sep 04 '20 at 13:20

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