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?
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7$\begingroup$ Possible duplicate of 1 2 3 4 5 6 7 8 9 = 100 $\endgroup$ – Omega Krypton Jan 30 '19 at 5:28
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$\begingroup$ This is impossible since only addition is allowed. $\endgroup$ – Embodiment of Ignorance Jan 30 '19 at 5:32
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$\begingroup$ Actually I think you can combine numbers like 3,4 can become 34 $\endgroup$ – Dptp90 Jan 30 '19 at 5:40
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1$\begingroup$ @OmegaKrypton No. The previous question allows many different operators; this one restricts to addition only. $\endgroup$ – Rand al'Thor Jan 30 '19 at 8:29
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$\begingroup$ why is there an addition tag? $\endgroup$ – Yout Ried Feb 6 '19 at 15:08
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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 $9$.
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$\begingroup$ 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 $\endgroup$ – North Jan 30 '19 at 6:57
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$\begingroup$ you have to add some text between each separate tag. If you want to add a newline in a spoiler, add <br> 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 $\endgroup$ – Flying_whale Jan 30 '19 at 9:07
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$\begingroup$ Turns out this was a way more interesting problem than the question lets on. $\endgroup$ – jafe Feb 7 '19 at 4:18
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The closest I can get is this:
90 + 1,765 + 8,234 = 99,999
Like north said also only a multiple of 9
