How Many Right Angles Do Clock Hands Form in 12 Hours?

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The discussion centers on determining how many times the big hand of a clock forms a right angle with the little hand over a 12-hour period. Participants initially suggest that the answer is 23, but it is clarified that the correct number is 22 times. The timing of these right angles depends on the starting point of the count, with specific times identified throughout the conversation. The participants utilize both intuitive reasoning and mathematical analysis to arrive at the conclusion, discussing angular velocities and the positions of the clock hands. A brute force method is also mentioned, where approximate times are listed for when right angles occur. The conversation includes some playful banter about the accuracy of calculations and the formatting of text for spoilers. Overall, the key takeaway is that the right angles occur 22 times, with a detailed breakdown of the approximate times provided.
  • #31


No problem.

Regards,

Mark
 

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