# Using only numbers 1,2,3,4,5,6,7,8,9,0 and addition,make up to the sum 100.using numbers only once?

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?

• Possible duplicate of 1 2 3 4 5 6 7 8 9 = 100 – Omega Krypton Jan 30 at 5:28
• This is impossible since only addition is allowed. – Embodiment of Ignorance Jan 30 at 5:32
• Actually I think you can combine numbers like 3,4 can become 34 – Dptp90 Jan 30 at 5:40
• @OmegaKrypton No. The previous question allows many different operators; this one restricts to addition only. – Rand al'Thor Jan 30 at 8:29
• why is there an addition tag? – Yout Ried Feb 6 at 15:08

## 2 Answers

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 $$9$$.

• 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 – North Jan 30 at 6:57
• 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 – Flying_whale Jan 30 at 9:07
• Turns out this was a way more interesting problem than the question lets on. – jafe Feb 7 at 4:18

The closest I can get is this:

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