Okay, I'll give a hint. I didn't see the other solutions either until I tried TD's proof. There's a subtle hint in his proof that can lead to the extra solutions. His proof isn't flawed, it simply contains an unspoken assumption that he made about the solutions.

-Dan

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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert