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 solution - spoiler by pcbouhid)

Only to show that 142857 was not a guess (or only a knowledge):

By (4), C3 coud only be 1 or 2. If you try C3 = 2, you'll see that it doesn't fit. So C3 = 1. And tracking the multiplicayion in (4), we'll find the number 142857 in the multiplicand.

Posted by pcbouhid on 2005-05-17 19:02:07