Sorry guys for the mistakes and confusion. I'm embarassed (no "oops" emoticon here to display it).

By "main diagonals" I meant both the

leading diagonal and

non-leading diagonal (aka

anti-diagonal). They're called "main" as opposed to the "broken diagonals". But after some research I think I've misused the term so from now on I'll only use the term

diagonal. Sorry again!

And of course I forgot to add the product of the 2 diagonals in my initial results. After a comprehensive check using Excel (and a resulting 32MB .xls file) I can confirm that JPF's range of 462..1321 is correct. Perhaps a bit surprising to me is if you don't count the diagonals (i.e. only 3 rows and 3 columns) the range become 436..947:

- Code: Select all
`Min = 436`

1 6 9

7 3 4

8 5 2

Max = 947

1 2 7

3 4 8

5 6 9

While you can rearrange the 436-grid to become the 462-grid, you can't do the equivalent for the 947-grid to become the 1321-grid. And while in many examples the min-grid and the max-grid are convertible to each other by the "10 minus" operation, it isn't the case here for both pairs. It is probably due to the usage of the multiplication operation.

Also from my Excel results I've confirmed 90 as the minimun largest product for the 3 rows & 3 columns in a grid. And 54 as the maximum smallest one. So for anybody who wants an encore of JPF's previous brainteaser:

Prove elegantly that there must always be at least a row or a column which has a product smaller than or equal to 54.