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Sam's Quick Sum

Age 7 to 11 Challenge Level:

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 $450 \times 1099 = 494550$.