The sum of three numbers is $2009$. The sum of the first two numbers is $1004$ and the sum of the last two is $1005$. What is the product of all three numbers?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem