many possible sequences

Are there many possible answers?

For example in the test example my program gets the answer:

0000 (do nothing)

0111 (insert 1 at the end)

1010 (change the last 1 in 0; I suspect that this 1 was initially a 0 and now, due to the noisy line, it's a 1)

1101 (erase the last 1)

the total sum of positions is 20, which is a multiple of 5 = 4 + 1

Did I get something wrong? I not, which solution should I print? And is it possible not to have any solution?