# A 3x3 grid of numbers with unique row and column ranges

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!

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.

• If you swap col1 and col2, the leading diagonal has range 3.
– JMP
Dec 30, 2019 at 16:24
• @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. Dec 30, 2019 at 16:51

It is

Possible

Because

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..