### First the puzzle:

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):

- The units digit has to be 1 for the result to end in 7
- The first digit has to be 2 to get 9 million and
something.

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.