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Let us switch the positions of the minute hand and the hour hand of a calassic clock with only 12 hours, not 24. Note that most of the time we will end up with an absurd configuration. But are there any valid such configuratins? If yes, count the number of valid configurations.

Till now i got only one configuration, 12:00. I considered 2 cases, if the clock is indicating a whole hour time, except 12:00, then it is a sure absurdity, because the hour hand will not directly point toward the time panel. Similar argument when it shows x:30. So i got only one solution 12:00. But still i am uncertain whether i have missed any and would like to know them and how ae any other solutions possible. Thanks in advance!

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  • $\begingroup$ There are obviously also all the tines (11 of them) when the two hands coincide. But answers to the linked question identify more. $\endgroup$ – timtfj Jan 20 '19 at 15:59
  • $\begingroup$ I suggest answerers answer the linked question. $\endgroup$ – timtfj Jan 20 '19 at 16:06