There are 4 persons A,B,C and D of which 2 are liars and 2 are knights. Each of these persons has a lucky and an unlucky number. All the 8 numbers are different and they are from 1 to 9 only. It is known that sum of lucky and unlucky numbers is same for all of these 4 persons and also sum of lucky numbers is greater than sum of unlucky numbers. Find the lucky and unlucky numbers for each of them if they made the following statements:
A:
C's lucky number is 7.
The missing number is 5.
B:
C's unlucky number is 4.
D's lucky number is 2.
C:
A is a liar.
B's lucky number is 6.
D:
The product of B's numbers is 24.
The maximum of all our numbers is A's lucky number.
Note: The missing number is the number from 1 to 9 which is not any one of these people's lucky or unlucky number.
(In reply to
Solution by Robby Goetschalckx)
"* missing number = 9.
This means A is a liar, C a knight. B's lucky
number must be 6, his unlucky number 3, which makes D a liar about the
product of B's numbers. B must be a knight, making C's unlucky number 4
and his lucky number 5. This gives a conflict with what A says about
this number."
This is not a conflict. If A is a liar, than 5 is not the missing number, nor is 7 C's lucky number. To continue your chain of logic here, B's numbers are 6 and 3, C's numbers are 5 and 4. If B is a knight, D's lucky number is 2, meaning his unlucky number is seven, leaving A with 8 and 1, and the missing number 9. The sum of lucky numbers exceeds the sum of unlucky ones, and all four add to 9.

Posted by Mark
on 20090802 06:25:45 