Junior Problem - Last fortnight's answer

Last week's question: Big product

Using the digits 1, 2, 3, 4, 5, 6 make two three-digit numbers and
multiply them together.  What is the biggest answer you can get?

The answer

I know that the digits in each number have to start with the biggest, and 6** x 5** (where * is a digit I don't yet know) is going to be at least 300000, whereas 6** x anything less than 500 is going to be smaller than this.  So I must have 6** x 5**.  There are only a few possibilities left to try, then: 643 x 521, 642 x 531, 641 x 543, 632 x 541, 631 x 542 and 621 x 543.  The biggest answer is then 348063.

Sadly, when I set the question, I got the answer wrong, so if you got it right and the computer said you were wrong, please give yourself a well-deserved pat on the back!

Julian