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.
First, there is : sum of lucky and unlucky numbers is same for all of these 4 persons
From a common man's perspective, if we sums up all the number, it sums to 45 or if those number could divide to 4 it supposed to be 44. Which leave us 1 as the missing number (45 mod 4 = 1)
That makes A as a liar and C as knights, also make b's lucky number is 6
A B C D
Liar Yes No
Lucky 6
Unlucky
if we assume D is knight then A's lucky number is 9, but then there is no product of 9 resulting 24, so D is a liar
then B is a knight, it will make C's unlucky number is 4, D's lucky number is 2.
A B C D
Liar Yes No No Yes
Lucky 6 2
Unlucky 4
then make all 4 person's lucky and unlucky number sums to 11
A B C D
Liar Yes No No Yes
Lucky 8 6 7 2 = 23
Unlucky 3 5 4 9 = 21
But with this result, it makes D's first statement is correct..
i am not sure that this is the solution, but nothing wrong with trying....

Posted by dimen
on 20090305 12:14:53 