These problems are from a very large set of questions about Liars who always lie about everything, and Knights who always tell the truth. Some questions also involve Knaves - people who strictly alternate between lying and telling the truth. (They are of course all indistinguishable from one another by outward appearance, and you must use logic to determine who's who.)
Alex, Bert, and Carl know a secret two digit number. It is known that one of them is a knight who always tells the truth, one is a liar who makes all false statements, and one is a knave who alternates between true and false statements. Each one of them makes statements about the number as follows:
Alex:
1: One digit is 1.
2: The sum of the digits is 8.
3: Bert's second statement is false.
Bert:
1: One digit is 3.
2: The difference of the digits is 4.
3: Exactly one of Carl's statements is true.
Carl:
1: One digit is 6.
2: Alex's first statement is false.
3: The first digit is larger.
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