logic puzzle solutions

Solution to the Puzzle of the Hyena's Alias: The Hyena's alias is "James Wilson". There are several ways to solve this puzzle, but perhaps the simplest is to realize that, if the fourth informant is correct, then the Hyena's alias must be either "John Moore" or "James Wilson". This is because each of the first two informants must be right about one of the names but not both, therefore one must be right about the first name and the other right about the surname. Then, the third informant's information allows us to eliminate "John Moore": since we've already ruled out "Taylor" as the last name of the alias, the third informant must be right that the first name is not "John".
Source: J. A. H. Hunter & Joseph S. Madachy, Mathematical Diversions (1975). The puzzle is based on one from page 49.

Solution to the Puzzle of the Masked Men: Benjy shot the guard. There are only eight possible distributions of truth-values, given that either all but one of the statements is true or all but one is false: four for each of the two possibilities depending on which of the four statements is the odd man out. So, to solve the puzzle, you can go through these possible distributions of truth-values until you've eliminated all but one.
An easier approach is to recognize that since Denny denies what Benjy said, their two statements must have opposite truth-values. This means that the other two statements are either both true or both false, thus eliminating four possible distributions. Suppose that Benjy spoke the truth and Denny was wrong. Then Charlie must be the guilty party, since Benjy accused him truly. That means that Charlie's own statement must be false, in which case Alfie's statement must also be false. However, since Charlie is the guilty party―and only one of the robbers shot the guard―Alfie is innocent, so his statement would be true. It's impossible for him to be both innocent and guilty, so the assumption that Benjy spoke the truth and Denny didn't must be mistaken.
Therefore, we can conclude that Benjy was wrong and Denny spoke the truth. So, Charlie isn't guilty after all. Suppose that Alfie and Charlie's statements are both false: then Alfie must be the guilty one, since he falsely claims innocence. However, if Alfie is guilty, then Charlie's statement was true, not false. Thus, the only remaining possibility is that all the statements were true except Benjy's. So, it's true that either Alfie or Benjy is guilty, since Charlie spoke the truth. However, it's not true that Alfie is guilty, since he correctly claimed innocence. Therefore, the guilty party must be Benjy.
Acknowledgment: The puzzle was suggested by one from Marilyn vos Savant's book Of Course I'm for Monogamy: I'm Also for Everlasting Peace and an End to Taxes (1996), pp. 164-165.


Solution to the Puzzle of the Dead Presidents: Johnson.
If the lie detector is accurate, then each of the five criminals said one truth and one falsehood. So, let's start by assuming that Kennedy's first statement is true and his second is false, and see what happens.
If Kennedy's second statement is false, then either Reagan or Johnson is the lookout. However, given that his first statement is true, Johnson is the mastermind. Thus, Reagan must be the lookout. Since Johnson is the mastermind, it follows that Kennedy isn't, which means that Nixon's second statement is true. Hence, Nixon's first statement is false, but that means that Nixon is the lookout. This contradicts the previous conclusion that Reagan is the lookout. Therefore, our original assumption must be wrong, which means that Kennedy's first statement is false and his second true.
Since Kennedy's first statement is false, Johnson is not the mastermind, and since his second is true, neither Reagan nor Johnson is the lookout. Because Kennedy's second statement is true, Ford's second statement is false, which means that his first is true. Since Ford's first statement is true, Reagan's second statement is false, which means that his first is true. So, Nixon is not the lookout, and his second statement is false, meaning that Kennedy is the mastermind. Since Nixon is not the lookout, it follows that Johnson is not the wheelman, by Modus Tollens from Ford's first statement. So far, we have been able to conclude that none of the following is the lookout: Kennedy (since he's the mastermind), Reagan, Johnson, and Nixon; this leaves only Ford. Thus, Johnson's second statement is true and his first is false. The only way for Johnson's first statement to be false is for neither Nixon nor Johnson to be the safecracker. So we now know that Johnson is not the mastermind (Kennedy), the lookout (Ford), the wheelman, or the safecracker. Therefore, Johnson is the triggerman.
By continuing this reasoning, you can determine the remaining two positions in the gang, but I'll leave this as an exercise for the reader.