The following pictures show n squares packed inside a unit circle, so that the total sum of the sides of the squares is as large as possible.

1. | 2. | 3. | ||

s = √2 = 1.414+ Trivial. | s = 4 / √5 = 1.788+ Trivial. | s = 2.331+ Found by Erich Friedman in June 2011. |

4. | 5. | 6. | ||

s = 2√2 = 2.828+ Found by Erich Friedman in June 2011. | s = 3.204+ Found by Maurizio Morandi in July 2011. | s = 3.597+ Found by Maurizio Morandi in July 2011. |

7. | 8. | 9. | ||

s = (2√10 + √190) / 5 = 4.021+ Found by Erich Friedman in June 2011. | s = (10√2 + 5√10 + √190) / 10 = 4.373+ Found by Erich Friedman in June 2011. | s = (10√2 + 3√10) / 5 = 4.725+ Found by Erich Friedman in June 2011. |

10. | 11. | 12. | ||

s = 4.970+ Found by Erich Friedman in June 2011. | s = 5.185+ Found by Maurizio Morandi in July 2011. | s = 5.419+ Found by Maurizio Morandi in August 2011. |

13. | 14. | 15. | ||

s = 5.720+ Found by Maurizio Morandi in August 2011. | s = 6.005+ Found by Erich Friedman in June 2011. | s = 6.218+ Found by Maurizio Morandi in July 2011. |

16. | 17. | 18. | ||

s = 6.435+ Found by Maurizio Morandi in July 2011. | s = 6.595+ Found by Maurizio Morandi in July 2011. | s = 6.816+ Found by Maurizio Morandi in July 2011. |

19. | 20. | 21. | ||

s = 7.069+ Found by David W. Cantrell in July 2011. | s = 7.271+ Found by Maurizio Morandi in July 2011. | s = 7.473+ Found by Maurizio Morandi in July 2011. |