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5 - Prime Factorizations

Andrew C. F. Liu
Affiliation:
University of Alberta
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Summary

Tweedledum told Alice, “The Queen of Hearts had put the Ace to Ten of Hearts in jail, ten days ago.”

“What had they done?” exclaimed Alice.

“Probably nothing,” said Tweedledee. “With Her Majesty, anything you do may be an offence. You are lucky if you still keep your head.”

“The Knave of Hearts had made an appeal to the King of Hearts, pleading the innocence of the prisoners,” said Tweedledum.

“What could His Majesty do?”

“Nothing that Her Majesty would not allow,” said Tweedledee.

“Ah!” said Tweedledum. “His Majesty had decided to be the Devil just this once, and unlocked all ten prison cells.”

“Hooray for His Majesty!” said Alice.

“His Majesty may live to regret this,” said Tweedledee, “or may not live to regret this.”

“His Majesty realized that too. So the next day, he went back to the jail. Starting with the second one, he relocked every second cell.”

“Were the Ace to Ten of Hearts placed in order in the cells?” asked Alice.

“Yes,” said Tweedledum.

“So now the Two, Four, Six, Eight and Ten of Hearts were locked up while the Ace, Three, Five, Seven and Nine were free,” said Tweedledee.

“Yes. On the third day, His Majesty had another change of mind. He started with the third cell, and altered the lock of every third cell.”

“What exactly did he do?” asked Alice.

“His Majesty would lock a cell if it was open, but unlock it otherwise. So now the Three and Nine of Hearts were locked up, but the cell of the Six of Hearts was unlocked again.”

“Knowing His Majesty,” said Tweedledee, “I bet he would continue in this manner for the next seven days.”

“Yes,” said Tweedledum. “Thus on the fourth day, he altered the lock of the fourth and the eighth cells, and today, he just altered the lock of the tenth cell. The latest news is that the Queen of Hearts has granted the prisoners a partial pardon, so that those whose cells are unlocked now are set free.”

“Who are the lucky prisoners?” asked Alice.

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Publisher: Mathematical Association of America
Print publication year: 2015

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  • Prime Factorizations
  • Andrew C. F. Liu, University of Alberta
  • Book: Arithmetical Wonderland
  • Online publication: 27 April 2017
  • Chapter DOI: https://doi.org/10.5948/9781614441199.008
Available formats
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Save book to Dropbox

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  • Prime Factorizations
  • Andrew C. F. Liu, University of Alberta
  • Book: Arithmetical Wonderland
  • Online publication: 27 April 2017
  • Chapter DOI: https://doi.org/10.5948/9781614441199.008
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Prime Factorizations
  • Andrew C. F. Liu, University of Alberta
  • Book: Arithmetical Wonderland
  • Online publication: 27 April 2017
  • Chapter DOI: https://doi.org/10.5948/9781614441199.008
Available formats
×