I'm studying for a cryptography test and I came across this question:
Assume a language has three letters: A=1111, B=0011 and C=1010. Two words in this language are encrypted with a one-time pad and by using the same binary key sequence. The first four bits for both corresponding cipher texts are, respectively: $C_1= 1110$ and $C_2=1000$. Determine the first letter of both corresponding plain texts as well as the first 4 bits of the key.
Isn't this question impossible to solve without additional information? Because:
$C_1 = L_1 + K + P_1$
$C_2 = L_2 + K + P_2$
Where $C_i$ is the cipher text, $L_i$ is the encrypted letter, $P_i$ is the one time pad and $K$ is the key.
Seeing how $L_1, L_2, P_1, P_2$ and $K$ are unknown, it's not possible to solve this, right? Or am I missing something?