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.

The number is 9. Bert answers correctly to all the questions and Alex lies.

Explanation...

Carl cannot be the one stating all the True statements, as he is contradicting his own statements. He says the number is at least 5 and also agrees that Alex's first statement is true... indicating that the number is 5. But Carl's first statement says that the number is even!!!

Hence, we are left with just 4 possibilities
1. Alex always says the truth AND Bert always lies
2. Alex always says the truth AND Carl always lies
3. Bert always says the truth AND Alex always lies
4. Bert always says the truth AND Carl always lies

Option 1
According to Alex's 3 statements AND Bert's 1st statement, the number has to be either 3 or 5 ... And Bert's 2nd statement confirms this! ... But all of Bert's statements have to be false ... Hence this option is not possible.

Option 2
Carl's last statement is true, while he is supposed to lie... Hence, this option is also not possible.

Option 3
Bert's first 2 statements indicate the number is 7 or 9. And since all of Alex's statements are false, the number should be 9.  For this to be true, Carl should have made just 1 correct statement ... and he does exactly that! (His second statement is the only one which is true)

Option 4
This option again is not possible as Bert says that Carl made a true statement.

Posted by Syzygy on 2007-03-18 01:57:42