The “sums of squares” competition category gives you a number, and your challenge is to find 2–4 integers whose sum of squares is equal to that number. It is always possible to do this!
For example, if the given number is \(2621\), any one of these would be a valid solution:
- \(2621 = 50^2 + 11^2\)
- \(2621 = 51^2 + 4^2 + 2^2\)
- \(2621 = 39^2 + 30^2 + 10^2 + 10^2\)
It can be difficult to train for this category, because there are many possible solutions, and it is slow to check whether yours is valid or a miscalculation. To help with this, below is a special practice tool.
Instructions
- Use a laptop or similar device with a keyboard.
- Select the number of digits you want in the target number.
- Write down up to 4 numbers whose sum of squares is equal to the target number.
- You can use the [Enter] or [Tab] key to move to the next box.
- You can use [Shift][Enter] to move to the previous box—for example, if you need to correct an answer.
- Leave the box empty if you don’t need to use it.
- You should press [Enter] again to submit your answer.
- The tool will check whether your answer is correct.
- If it is wrong, it will calculate your sum of squares, so you can compare it.