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What period of time has the least weight?

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What period of time has the least weight?
posted Dec 28, 2023 by Vishal

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There are 12 people and a seesaw on an island, and you have the following information:

  • There is one islander who weighs differently than the other 11, but you don't know which one, nor if they are heavier or lighter.
  • You may use the seesaw to compare the weights of any two sets of islanders of your choosing.
  • Each of the twelve islanders is uniquely identifiable and can be weighed more than once.

What is the least number of times you need to use the seesaw in order to guarantee that you can identify the person who has the different weight?

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A grandfather clock chimes the appropriate number of times to indicate the hour, as well as chiming once at each quarter hour. If you were in another room and heard the clock chime just once, what would be the longest period of time you would have to wait in order to be certain of the correct time?

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