Alex, Bert, and Carl know a specific number 1 to 9. From the statements below can you determine the number knowing one of them made three true statements and one of them made three false statements?

Alex: The number is less than or equal to 5.
Bert: The number is 2, 4, 7, or 9.
Carl: The number is even.
Alex: Bert's first statement is false.
Carl: The number is at least 5.
Bert: The number is odd.
Carl: Alex's first statement is true.
Alex: The number is not 1, 2, 8, nor 9.
Bert: Carl made exactly one true statement.

Bert said 3 true statements.

Alex said three false statements.

Carl said two false statements and one true statement.

Assuming that Bert made three true statements, you know that the number is 2 4 7 or 9, the number is odd, and carl made exactly one true statement.   Knowing this the possibilities are cut to either 7 or 9.

Assuming that Alex made three false statements, you know that the number is greater than 5,bert's first statement is true, andthe number is 1 2 8 or 9.   Kowing this the pnly possibility is 9.

Since Carl only made one true statement,according to bert who made three true statements, the first and last statements must  be  false because the number is not even and alex's first statement was not true.  This leaving the second statements to be true saying that the number is at least 5.

 

Therefore, the answer is 9.

Posted by shaban on 2007-03-17 09:18:59