Place the numbers 1 through 9 in the grid below:

   1 2 3  
A |_|_|_|  
B |_|_|_|  
C |_|_|_|  
 

1. The product of the numbers in row C is twice the sum of the numbers in row C.
2. The product of the numbers in column 3 is twice the sum of the numbers in column 3.
3. If you ignore column 1, all the columns have even products.
4. If you take the six-digit number C3 B3 B1 C1 A3 B2 and multiply it by 3, you get the six-digit number B3 B1 C1 A3 B2 C3.

Try to figure it out without using a computer program.

The clue (4) is the key.

C3 B3 B1 C1 A3 B2  is the famous number 142857. It can be obtained using clue (4).

By (1) ===> C2 = 3.

by (3) ===> A1 = 9 and A2 = 6.

Final grid :

9...6...5

2...7...4

8...3...1

 

Posted by pcbouhid on 2005-05-17 18:45:02