Why doesn't Fano's method work?

Question

IT education

We analyzed the following problem:
Messages containing only 4 letters A, B, C, D are transmitted over the communication channel;
for transmission, a binary code is used that allows unambiguous decoding.
For letters A, B, C, the following code words are used:А: 000111, Б: 111, В: 1010 .
Specify the shortest code word for the letter G, under which the code will allow unambiguous decoding.
If there are several such codes, indicate the code with the smallest numerical value.
By Fano's condition, the solution is 01, but it is written in the answers 00(but the code of the letter A starts with 00!), and it was not possible to choose a sequence that would be ambiguously decoded with such a cipher ...
Please help me figure it out: we are not catching up with something Or is it still a typo?

Answer 1

Stupidly sorting out

Г : 0  ->  ГГГБ неотличимо от А
Г : 1  ->  ГГГ неотличимо от Б
Г :00  ->  ни Г, ни ГГ не дают такого префикса, чтобы он, слившись с любой/любыми
                последующими буквами, выглядел как код/набор кодов других букв.

Answer 2

Perhaps the answer is not very timely, but for the future.
In this case, it is not indicated which Fano condition (direct or inverse) should work, so we check both.
Directly, the best answer is indeed 01 (not the beginning of other codewords), and backwards - 00 (not the end of other codewords).