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.

Calling (B3 B1 C1 A3 B2 C3) N, we have :

(N - C3)/10 + 10^5 * C3 = N/3

wich leads to N = [3 * (10^6 - 1) * C3] / 7

3*(1,000,000 - 1) = 3*999,999=2,999,997

N = 2,999,997 * C3 / 7

N = 428,571 * C3  ====> C3 = 1 ====> N = 428,571

N/3 = 428,571 / 3 = 142,857 = (C3 B3 B1 C1 A3 B2)

The rest follows...

Edited on March 24, 2009, 6:13 pm

Posted by pcbouhid on 2005-05-18 01:08:13