A,B & C are 7-digit numbers, each being a permutation of 1234567.

If written in three rows, one below the other, the resulting column-wise sums
(i.e a_i+b_i+c_i) will be square numbers.

Given A=2461357, find B and C.
Rem: Since B and C are interchangeable - there will be only one basic solution.

The sum of each column will be greater than or equal to 3, and less than or equal to 21.  So each column will have to sum to either 4, 9, or 16. 

Also, the total of all columns will have to be (1+2+3+4+5+6+7) * 3 = 84.  The only way to do this is to have three columns sum to 16, and four columns sum to 9.  This adds an extra restriction which makes the puzzle a little easier to solve.

A little trial and error produced the following solution:

A = 2461357

B = 3217654

C = 4321765

 

Posted by tomarken on 2014-07-02 11:56:22