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.

I started with row c and column 3.  They had to be 1,3,8 and 1,4,5, this made c3=1.  I tentatively penciled the other digits.  Realizing the x/7 pattern of the same six digits repeating in order, I noticed in clue 4 the patterns were the same six digits in order.  On a gamble, with c3=1 that made the first pattern 142857 and the second 428571 (of course they may not have been the x/7 pattern at all, but) when it worked out, it became easy to figure out the last two digits of 6 and 9 which can be in either order.  I really liked this problem.  I am like you Dustin, I like to figure them out without a computer.

Posted by john on 2005-06-06 20:59:12