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 2009-03-05 12:14:53