The following pictures show n unit squares packed inside the smallest known domino (of shortest side length s).

1-2

s = 1

Trivial.

3

s = 3/2 = 1.5

Trivial.

4

s = 1.930+

Found by Evert Stenlund

in June 2010.

5-8 s = 2 Trivial. | 9 s = 2 + √2/3 = 2.471+ Found by Evert Stenlund in June 2010. | 10 s = 5/2 = 2.5 Trivial. |

11 s = 2.779+ Found by Evert Stenlund in June 2010. | 12 s = 6 (1 + √2) / 5 = 2.897+ Found by Maurizio Morandi in June 2010. | 13 s = 2.976+ Found by David W. Cantrell in July 2012 (after Maurizio Morandi in June 2010.) |

14-18 s = 3 Trivial. | 19 s = 3 + 1/√5 = 3.447+ Found by Maurizio Morandi in June 2010. | 20-21 s = 7/2 = 3.5 Trivial. |

22 s = 3.745+ Found by David W. Cantrell in July 2012 (after Maurizio Morandi in June 2010.) | 23 s = 3.849+ Found by Maurizio Morandi in June 2010. | 24 s = 3.882+ Found by DC after MM in August 2012. |

25 s = 3.939+ Found by DC after MM in August 2012. | 26 s = 3.981+ Found by David W. Cantrell in July 2012 (after Maurizio Morandi in July 2012.) | 27-32 s = 4 Trivial. |

33 s = 3 + √2 = 4.414+ Found by Maurizio Morandi in July 2012. | 34 s = 4 + √2/3 = 4.471+ Found by David W. Cantrell in July 2012. | 35-36 s = 9/2 = 4.5 Trivial. |

37 s = 10 / 3 + √2 = 4.747+ Found by Maurizio Morandi in August 2012. | 38 s = (13 + √2) / 3 = 4.804+ Found by Maurizio Morandi in August 2012. | 39 s = 4.839+ Found by David W. Cantrell in August 2012. |

40-41 s = (10 + 7√2) / 4 = 4.974+ Found by David W. Cantrell in August 2012. | 41-42 s = 4.989+ Found by David W. Cantrell in August 2012. | 43-50 s = 5 Trivial. |