I'm studying for a cryptography test and I came across this question: 

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> *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.*
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Isn't this question impossible to solve without additional information? Because:

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> $C\_1 = L\_1 + K + P\_1$
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> $C\_2 = L\_2 + K + P\_2$
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> 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.
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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?