Riddles!

[TheGoldenGriffin]

Im asking if my situation is solvable because i tried a bunch of ways to solve it but failed. If you guys CAN find a way to find the odd head from that, then my solution is valid (hopefully), its the missing step that will have everything fit together perfectly(possibly), like the Higgs boson(in a way).

If it helps, i have these steps: (its easier to read if you quote, remove the white color code, and preview)

Weigh 2 vs 2. If tilt, go to A. If even, go to B
A: If tilt, swap a pair of heads. If…
… it tilts the same way, you didn't move the odd one. Remove one side, replace with 2 unweighed ones (you know those are safe) and weigh. If even, you took the odd one out, which is the one you didn't swap. If tilt, the one you swapped that is still on the balance is the odd one.
… it tilts the other way, you moved the odd one to the other side, the head you move is the odd one. Remove one side, replace with 2 unweighed ones (you know those are safe) and weigh. If even, you took the odd one out, which is the one you swap. If tilt, the one you swapped that is still on the balance is the odd one.

B: If even, group the 4 heads together, you know all 4 is safe. There are 8 left, take 6 of them and put 1 with the 4 and other 5 on the other side, so you have 5 vs 5 and weigh. If…
… even, the 1 of the 2 you left out is the of one and you know all 10 weighted is safe. Weigh 1 safe vs 1 left. If even, the one left unweighted is the odd one. If tilt, the one left weighted is the odd one
… tilt, this is where the problem is