Congratulations to Jamie, St Angela's
School, Forest Gate, London; Joshua, Amptill, Bedfordshire; Sohail,
Predesh, Gurpreet, Jessica and James, Jack Hunt School,
Peterborough; Charlotte, Helen, Bella, Charis, Christianne, Peach,
Sheila, Cheryl, Pen and Lyndsey, Laura and Emma, The Mount School,
York. Here is Jamie's solution:
There are $900$ numbers between $100$ and $999$ so you can
halve the number $900$ to see how many pairs you get.
Each pair adds up to $1099$ because if you add $100$ to $999$
the answer is $1099$ and if you add $101$ to $998$, or $102$ to
$997$ and so on you get the same answer.
The sum of all the three-digit numbers is $450 \times 1099 =