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!
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asked Dec 30, 2019 at 14:44
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2 Answers
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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.
answered Dec 30, 2019 at 15:04
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2$\begingroup$ If you swap col1 and col2, the leading diagonal has range 3. $\endgroup$– JMPCommented Dec 30, 2019 at 16:24
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$\begingroup$ @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. $\endgroup$ Commented Dec 30, 2019 at 16:51
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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..
