Its pretty easy to take 16 L-triominoes and make a giant L-triomino that is 4x scale, like in this classic triomino puzzle.

But consider the four possible orientations of the L-triomino.
Is it still possible to make the 4x scale triomino if we require that only three orientations of the individual triominoes be present in the solution?

Jer's solution made me realize I had a bug, 

since my "complete" search missed his. 

Thanks! Now (once again) I think I found all unique 

solutions. Note, due to symmetry across the diagonal, 

solutions 1,2,3 below are reflections of 6,5,4 respectively.

The program in the previous link is updated. 

----------------------------------------

  XX     This is the missing pattern
  X 

    Pattern list key:

0 = XX    1 = X     2 =  X
     X        XX        XX

1. Pattern list: 0011101200021112

0011    
2031    
2233    
4556    
44566788
99AA77B8
C9DAEBBF
CCDDEEFF


 ----------------------------------------

  X      This is the missing pattern
  XX

    Pattern list key:

0 = XX    1 = XX    2 =  X
    X          X        XX

2. Pattern list: 0110220202020202

0011    
0221    
3324    
3544    
55667889
AA677899
ABCCDEEF
BBCDDEFF

3. Pattern list: 0022011202020202

0011    
0213    
2233    
4455    
46657889
AA677899
ABCCDEEF
BBCDDEFF

4. Pattern list: 0022002102102202

0011    
0213    
2233    
4455    
46577889
66AA7899
BBCADEEF
BCCDDEFF

5. Pattern list: 0022002201102022

0011    
0213    
2233    
4455    
46578899
66778AA9
BBCDDEAF
BCCDEEFF


 ----------------------------------------

   X     This is the missing pattern
  XX

    Pattern list key:

0 = XX    1 = XX    2 = X 
    X          X        XX

6. Pattern list: 0102022121121221

0011    
0221    
3244    
3345    
67755899
667AA889
BCCDAEFF
BBCDDEEF

lord@rabbit 12471 % 

Edited on October 10, 2021, 3:31 am

Posted by Steven Lord on 2021-10-09 22:16:57