L's in Squares
The following pictures show n L's with short side 1 inside the smallest known square (of side s ).

1.

s = 2
Trivial.
  		           2.

s = 3
Trivial.
  		           3.

s = (3 + 3√2) / 2 = 3.621+
Found by Serhiy Grabarchuk
in July 2005.

4.-5.

s = 4
Trivial.
  		           6.

s = 7 / √2 = 4.949+
Found by Erich Friedman
in June 2005. 		           7.-8.

s = 5
Trivial.
 

9.

s = 5.81901+
Found by Junzhe You
in October 2026. 		           10.-12.

s = 6
Trivial.
  		           13.

s = 4 + 2√2 = 6.828+
Found by Maurizio Morandi
in June 2012.

14.-16.

s = 7
Trivial.
  		           17.

s = 19/3 + √2 = 7.747+
Found by Maurizio Morandi
in June 2012. 		           18.

s = 13/2 + √2 = 7.914+
Found by Maurizio Morandi
in June 2012.

19.-21.

s = 8
Trivial.
  		           22.

s = 3 + 4√2 = 8.656+
Found by Maurizio Morandi
in June 2012. 		           23.

s = 15/2 + √2 = 8.914+
Found by Maurizio Morandi
in June 2012.

24.-27.

s = 9
Trivial.
  		           28.

s = 9.79450+
Found by Joshua Wolk
in September 2026. 		           29.

s = 27/4+9√2/4 = 9.93198+
Found by Yanis Gomes
in October 2026.

29.-33.

s = 10
Trivial. 		           34.

s = 10.76777+
Found by Joshua Wolk
in September 2026. 		           35.

s = 10.86965+
Found by Joshua Wolk
in September 2026.

36.-40.

s = 11
Trivial. 		           41.

s = 11.76777+
Found by Joshua Wolk
in September 2026. 		           42.

s = 11.87132+
Found by Joshua Wolk
in September 2026.

43.-48.

s = 12
Trivial. 		           49.

s = 12.79450+
Found by Joshua Wolk
in September 2026. 		           50.

s = 12.86396+
Found by Joshua Wolk
in September 2026.