# A new year's mathematical mystery

Sam, Magnus, and Olivia each try to write the number 2020 as the sum of consecutive positive integers.

They each use more than one integer, a different number of integers to the others, and none of the same integers as the others.

How many integers did they write overall? How do you know?

This can be done without a computer programme.

• 4 solutions for 3 people – sudhackar Jan 13 at 11:52
• ah, my mistake. 'At least one' should read 'more than one'. Fixed. – JThistle Jan 13 at 13:56

$$249,250,251,252,253,254,255,256=4\times505$$
$$31,\dots,50,51,\dots,70=20\times101$$
$$2020$$

$$49$$ integers in total.

Another solution is:

$$402,403,404,405,406=5\times404$$ (@Annosz)

The solutions correspond to:

the odd divisors of $$2020$$, namely $$1,5,101$$ and $$505$$.

• rot13(Gurer vf ng yrnfg bar bgure fbyhgvba, fgnegvat sebz sbhe uhaqerq gjb) – Annosz Jan 13 at 11:42
• Yep, sorry about the question: 2020 is not a sum of consecutive integers, since it's not a sum. The question should have made that clearer and has been updated. – JThistle Jan 13 at 13:58