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Santa's Dirty Socks


Santa needs help to find his dirty socks, hidden in a single box that is heavier than the rest among 1024 boxes. By eliminating half of the boxes at a time, he can quickly narrow down to the box containing his dirty socks.

Questions:

  • How many weighings would the process take if there were 2048 boxes?
  • How many more weighings are needed if there are twice as many gifts?
  • What if there are 4 times as many gifts?
  • What if there are 1024 times as many gifts?
  • How many gifts can be checked in 30 weighings?
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