26144

To NRICH,
We worked this out in class together : Sophia, Elise and I.

Here is our suloution:

1+2+3 = 6 It is a multiple of 3 - there are three digits to add.
2+3+4 = 9 It is also a multiple of 3
3+4+5 = 12 another multiple of 3

You can do this with any ODD numbers and it will always equal a multiple of however many numbers you've used:

1+2+3+4+5 = 15 a multiple of 5

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However, if you do this with any even amount of numbers, it will equal something different.

2+3+4+5=14. That's a multiple of 2 and 2 is half of 4; 4 is the number of numbers.

It's the same idea with any even number you test it with:

1+2+3+4+5+6+7+8=36. Half of 36 is is a multiple of 4 whicch is half of 8! There arev 8 digits to add up!