When a five-digit number, with "1" as the thousands digit, is multiplied by 4 1 7 the result is a seven-digit number which begins with 9 and ends 0 5 7. Find the missing digits for both these numbers.

Here's the Excel file: X marks the Spot.xls (Right-click on the link, "Save Target As", and select where you want the file to be saved).

The increment buttons (called spinners in Excel) change the values of the digits, and automatically produce new results for the multiplication.

The answer to the puzzle is 2 1 9 2 1 but a class are very unlikely to get that just by flicking though digit values.

Many of us tackle this kind of puzzle with a mixture of reasoning and trial and error (or trial and improvement):

Even when we hit upon a solution by trial and error, it's good to ask whether we can now see a reason why that had to be the answer.