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Mailbox: Logic Puzzle - Liars in England - Solution
Contributed by a reader

It was recently pointed out to me that my logic was flawed and I had the wrong answer here. While I hung my head in shame, I figured out the right answer...I think.

Like with a great many logic puzzles, the way to solve this puzzle is by eliminating variables until you have only one possible solution left.

The four true statements...
Smith can't be only telling the truth because he states both Jones and Robinson make only true statements, which means that all three of them would only make true statements. This has to be incorrect because some of the statement made are conflicting.

Jones can't make all true statements because he states that all of Smith's statements are untrue. This must be false because Smith states that all of Jones' statements are true, which would be false if Jones' statement was truth.

Therefore, Robinson must be the one who makes four true statements.

Since Jonesí 4th statement has been proven false, and his 2nd statement must also be false, since it conflicts with Robinsonís 1st statement, then Jonesí correct statements are #1 and #3. Robinsonís 2nd statement and Jonesí 3rd statement are a trick Ė he can be both British and Dutch.

For Smithís statements, only #3 is true. Since we know that Jonesí #1 is correct, then Smithís #1 must be false. The same reasoning applies to #2. And we already know that #4 is false.

 
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