Sorting Numbers

Alice has 9 numbers and wants to sort them in increasing order: \[7, 8, 2, 9, 5, 1, 8, 5, 3.\] It should be an easy task, but Alice only knows how to sort 6 numbers! Therefore, she does the following:

  • Sort the first 6 numbers to get \({\color{red}1, 2, 5, 7, 8, 9}, 8, 5, 3.\)
  • Sort the last 6 numbers to get \(1, 2, 5, {\color{red}3, 5, 7, 8, 8, 9}.\)
  • Sort the first 6 numbers again to get \({\color{red}1, 2, 3, 5, 5, 7}, 8, 8, 9.\)

Finally, it sorts the 9 numbers! Does this method work for any 9 numbers?

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