Riddles!

[TheGreatErenan]

Yes.

Here's Gf!sh's solution in greater detail:


Label the twelve tiki heads with letters A - L.

1. Weigh ABCD vs. EFGH (1st weighing). If...
   
   1. ABCD < EFGH, then IJKL are clean, and either ABCD contains a light head or EFGH contains a heavy head. Go to 2.
   2. ABCD > EFGH, then IJKL are clean, and either ABCD contains a heavy head or EFGH contains a light head. Go to 3.
   3. ABCD = EFGH, then ABCDEFGH are clean, and EFGH contains either a heavy head or a light head. Go to 4.
      
2. Weigh ABEF vs. CGIJ (2nd weighing). If...
   
   1. ABEF < CGIJ, then CEF are clean, and either AB contains a light head or G is a heavy head. Go to 5.
   2. ABEF > CGIJ, then ABG are clean, and either EF contains a heavy head or C is a light head. Go to 6.
   3. ABEF = CGIJ, then ABCEFG are clean, and either D is a light head or H is a heavy head. Go to 7.
      
3. Weigh ABEF vs. CGIJ (2nd weighing). If...
   
   1. ABEF > CGIJ, then CEF are clean, and either AB contains a heavy head or G is a light head. Go to 8.
   2. ABEF < CGIJ, then ABG are clean, and either EF contains a light head or C is a heavy head. Go to 9.
   3. ABEF = CGIJ, then ABCEFG are clean, and either D is a heavy head or H is a light head. Go to 10.
      
4. Weigh IJ vs. AK (2nd weighing). If...
   
   1. IJ < AK, then either IJ contains a light head, or K is a heavy head. Go to 11.
   2. IJ > AK, then either IJ contains a heavy head, or K is a light head. Go to 12.
   3. IJ = AK, then IJK are clean, and L is either a light head or a heavy head. Go to 13.
      
5. Weigh A vs. B (3rd weighing). If...
   
   1. A < B, then A is a light head.
   2. A > B, then B is a light head.
   3. A = B, then G is a heavy head.
      
6. Weigh E vs. F (3rd weighing). If...
   
   1. E < F, then F is a heavy head.
   2. E > F, then E is a heavy head.
   3. E = F, then C is a light head.
      
7. Weigh A vs. D (3rd weighing). If...
   
   1. A > D, then D is a light head.
   2. A = D, then H is a heavy head.
   3. A < D, then either the universe broke or you have been spontaneously transported into an alternate universe in which the only difference is which one of your tiki heads is heavy or light.
      
8. Weigh A vs. B (3rd weighing). If...
   
   1. A < B, then B is a heavy head.
   2. A > B, then A is a heavy head.
   3. A = B, then G is a light head.
      
9. Weigh E vs. F (3rd weighing). If...
   
   1. E < F, then E is a light head.
   2. E > F, then F is a light head.
   3. E = F, then C is a heavy head.
      
10. Weigh A vs. D (3rd weighing). If...
    
    1. A < D, then D is a heavy head.
    2. A = D, then H is a light head.
    3. A > D, then either the universe broke or you have been spontaneously transported into an alternate universe in which the only difference is which one of your tiki heads is heavy or light.
       
11. Weigh I vs. J (3rd weighing). If...
    
    1. I < J, then I is a light head.
    2. I > J, then J is a light head.
    3. I = J, then K is a heavy head.
       
12. Weigh I vs. J (3rd weighing). If...
    
    1. I < J, then J is a heavy head.
    2. I > J, then I is a heavy head.
    3. I = J, then K is a light head.
       
13. Weigh A vs. L (3rd weighing). If...
    
    1. A < L, then L is a heavy head.
    2. A > L, then L is a light head.
    3. A = L, then whoever told you that exactly one of your heads weighed differently from the others was lying.