Weekly Problem 14 - 2011
The sum of the first two numbers and the last two numbers is
$1004+1005=2009$. This counts the middle number twice. But the sum
of all three numbers is $2009$, so the middle number is $0$. Hence
the product of all three numbers is $0$.
[Alternatively: Let the three
numbers be a, b and c.
We have
$a+b=1004$
$b+c=1005$
and
$a+b+c=2009$
Adding the first two
equations gives
$a+2b+c=2009$
and subtracting the third
equationg from this gives
$b=0$
Thus the product
$abc=0$.]