Problem #26

This month's problem is a logic puzzle. Four mathematicians make the following statements:

Alice: "I am insane."
Bob: "I am pure."
Charlie: "I am applied."
Dorothy: "I am sane."
Alice: "Charlie is pure."
Bob: "Dorothy is insane."
Charlie: "Bob is applied."
Dorothy: "Charlie is sane."

Describe the four mathematicians, given that:

Source: Mathematics and Informatics Quarterly (via Tom Halverson)

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