Can you place every number from 1 to 9 into a 3x3 grid such that the range of every row and column is a unique value? The range of a row is the difference between its maximum and minimum values (similarly for columns).

Good luck!


2 Answers 2


Here is one solution:

 1 3 9   8
 5 7 6   2
 4 8 2   6
 4 5 7

I solved it by

first placing the 1 and 9 in one row, to get the largest range. The next numbers I placed were 2, 8, 3, 7, 4, 6, 5. In other words I worked from the outside (largest/smallest) inwards. Each time I tried to place the number such that a new row/column would provide the next missing range or do nothing.

  • 2
    $\begingroup$ If you swap col1 and col2, the leading diagonal has range 3. $\endgroup$
    – JMP
    Dec 30, 2019 at 16:24
  • $\begingroup$ @JMP That is nice. Of course it is impossible for both diagonals to take part since the only possible ranges are 2 to 8, i.e. just 7 possible values. $\endgroup$ Dec 30, 2019 at 16:51

It is



1 3 9
4 5 8
7 6 2

Will do.. and I just trying to place them one by one and find this with no difficulty..


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