Five criminals appeared before the court for sentence.
Their names,
strange to say, were Fraud, Libel, Blackmail, Theft and Murder - each
the namesake of the crime with which one of the others was charged.
The namesake of the crime with which Blackmail was charged was himself
charged with the crime of which the namesake was charged with murder.
The namesake of the crime with which Murder was charged was himself
charged with the crime of which the namesake was charged with fraud.
All the prisoners were found guilty and sentenced. Theft, for
example, got seven years. The criminal who was found guilty of murder was placed on death row.
Who committed the murder?
The solution is Libel.
A pictorial representation of the problem can illustrate the solution relatively simply.
If there are five crimes and five names, and no one can be guilty of the crime for which they are named, then it can be simplified into five nodes - M, T, L, F, B. Saying Theft was charged with fraud is illustrated by an arrow from T to F.
In this way we can establish that, due to the number of nodes (5), the only possible configurations involve either one cycle of all 5, or two separate cycles of 2 and 3. A cycle of 4 is not permitted as this would result in the one remaining node having to loop back and point to itself, which would be the same as a criminal being charged with the crime they are named for.
From this layout, one can take the next 2 statements and represent them as B -> a -> b -> M, and M -> x -> y -> F.
This tells us that M -> B or M -> F are not possible, because this would create a closed cycle of 4, which we know from above would violate the first statement.
If M cannot connect to M, B or F, and as the last clue says, Theft got seven years, and not the death sentence, the only remaining option is L - Libel.
Solution
