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.

(In reply to x/7ths by jduval)

The only mistake you did was "the last two digits of 6 and 9, which can be in either order".

The order must be 9...6..., since 6....9...would make the product of the second column odd, contradicting clue (3). 

Posted by pcbouhid on 2005-06-06 21:33:44