# 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 Jan 13 '20 at 11:52
• ah, my mistake. 'At least one' should read 'more than one'. Fixed. Jan 13 '20 at 13:56

$$402,403,404,405,406=404\times5$$
$$31,\dots,50,51,\dots,70=20\times101$$
$$249,250,251,252,253,254,255,256=4\times505$$
$$53$$ integers in total.
the odd non-trivial divisors of $$2020$$, namely $$5,101$$ and $$505$$.