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In Sum-mary

Stage: 3 Short Challenge Level: Challenge Level:1

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 
and     $a+b+c=2009$
Adding the first two equations gives
and subtracting the third equationg from this gives
Thus the product $abc=0$.]


This problem is taken from the UKMT Mathematical Challenges.