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Using only the numbers

1, 2, 3, 4, 5, 6, 7, 8, 9 and 0

With only addition can you make a sum of 100?

Glorfindel
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Hamish Penlington
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2 Answers2

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This is mathematically impossible. I think EmbodimentofIgnorance was trying to tell us this, but didn't explain it.

Basically, no matter what order you try to put the answers into, it'll never actually become $100$ — it'll always be $99$, because the numbers add up to be multiples of nine. Consider this:

When you add up all numbers $0$–$9$, it'll be $45$ — a multiple of $9$.
Now obviously, $45$ is too small, so you're gonna have to make some two digit numbers (e.g. $45$, $67$, $13$, etc.)

Now this gets a little funky, so bear with me.

Let's assume you use the value of $34$ instead of $3+4$. You'll notice that you'll get a multiple of nine when you subtract the number by the ones you were using (so $34-3-4=27$).

Now, going back to the total, it becomes $45-3-4+34 = 72$.

You subtract the three and the four, because those numbers are being used for $34$. Keep in mind that order doesn't matter, because it's essentially just $45-7$.
No matter what pair you decide to choose, it'll always turn out to be a multiple of $9$.

user46002
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Prince North Læraðr
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  • AHHHHHH omg I swear I've been using se for a year now and I still can't use spoiler tags correctly. How do you put multiple of them without it glitching – Prince North Læraðr Jan 30 '19 at 06:57
  • you have to add some text between each separate tag. If you want to add a newline in a spoiler, add
    but don't use "enter" or it will glitch. edit: looking at the edit, it seems there're several method to achieve this. apparently you can add a new spoiler tag on each newline to add multiline spoiler     – Flying_whale Jan 30 '19 at 09:07
  • Turns out this was a way more interesting problem than the question lets on. – Jafe Feb 07 '19 at 04:18
4

The closest I can get is this:

90 + 1,765 + 8,234 = 99,999
Like north said also only a multiple of 9

Doomenik
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