Sumigahara Uguisu no Ronshou

Uguisu stands out from ordinary teenage girls. Spending most of her time in the library and never appearing in class, she still somehow manages to score full marks in tests. Though she is difficult to deal with at times, I developed a strange relationship with her.
One day we were entrusted a strange order to investigate whether the genius mathematician Kiryu is actually a magician. We then went to the Kirin Mansion, the place where professor Kiryu resides. And then two days later, professor Kiryu became a headless corpse. Though the suspects are limited, the intriguing results shows that everyone here are clean!? Is the professor really a magician? Is this really a murder case? Are there any victims? Is there an actual culprit?
These doubtful questions will be directed against through different “logical arguments.”