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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.

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    $\begingroup$ 4 solutions for 3 people $\endgroup$ Commented Jan 13, 2020 at 11:52
  • $\begingroup$ ah, my mistake. 'At least one' should read 'more than one'. Fixed. $\endgroup$ Commented Jan 13, 2020 at 13:56

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$402,403,404,405,406=404\times5$
$31,\dots,50,51,\dots,70=20\times101$
$249,250,251,252,253,254,255,256=4\times505$

$53$ integers in total.

The solutions correspond to:

the odd non-trivial divisors of $2020$, namely $5,101$ and $505$.

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  • $\begingroup$ rot13(Gurer vf ng yrnfg bar bgure fbyhgvba, fgnegvat sebz sbhe uhaqerq gjb) $\endgroup$ Commented Jan 13, 2020 at 11:42
  • $\begingroup$ 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. $\endgroup$ Commented Jan 13, 2020 at 13:58

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