Sam's quick sum
What is the sum of all the three digit whole numbers?
Age
7 to 11
Challenge level
Problem
What is the sum of all the three-digit whole numbers?
Getting Started
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ... | 97 | 98 | 99 |
| 99 | 98 | 97 | 96 | 95 | 94 | 93 | ... | 3 | 2 | 1 |
| 100 | 100 | 100 | 100 | 100 | 100 | 100 | ... | 100 | 100 | 100 |
Student Solutions
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 $450 \times 1099 =
494550$.
Teachers' Resources
Why do this problem?
This problem is a good context in which to discuss different,
and perhaps most efficient, methods of calculation.
Key questions
Why don't you try adding all the one-digit numbers
first?
Can you describe what you did?
Are there any quicker ways of doing it?
Possible support
Learners could find the sum of the one-digit whole numbers
first and then the two-digit whole numbers instead.