Question

What is the sum of `1+2+3+4+5+6+7+8+9+1234567890+9876543210+99999999+(0xx9001)-9999999+(-999999999)`?

I want to know

Answer 1

`211111145`

Explanation:

This is a test to see if you spot thing and give you practice of splitting your solution up into smaller parts.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider `1+2+...+8+9`

Take the outermost values and pair them then work your way in.

`9+1=10`
`8+2=10`
`7+3=10`
`6+4=10`
Then there is 5

`color(blue)(=> 4xx10+5=45)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider `1234567890+9876543210`

Write as
`" "1234567890`
`ul(" "9876543210+`
`color(white)(.)1 1111111100`

So the questions sum from the left to this point is:

`color(blue)(45+1111111100+...+)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider `+99999999 + (0xx9001) - 9999999`

`0xx9001 = 0` so we can totally forget about that as it is part of addition so has no effect.

So now we have

`99999999`
`ul(color(white)(9)9999999)" "larr" this is a negative value"=>Subtract`
`90000000`

So the questions sum from the left to this point is:

`color(blue)(45+1111111100+90000000+...+)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the last value `+(-999999999)`

Plus and minus together like this make a minus so we have

So the questions sum from the left to this point is:

`45+1111111100+90000000-999999999`

So the last two numbers can be written as
`color(white)(9)90000000`
`ul(999999999) larr" negative value => subtract"`

There are different ways of dealing with this. This is just one way

`999999999 larr "Negative value"`
`ul(color(white)(9)90000000) larr "Positve value but subtract it"`
`900000000 larr "Negative answer"`

So the questions sum from the left to this point is:

`color(blue)(45+1111111100-900000000)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the last two from the previous part solution

`+1111111100-900000000`

`1111111100`
`ul(color(white)(1)900000000 )larr" negative value so subtract"`
`color(white)(0)211111100`

`color(blue)(45+211111100color(green)(= 211111145)`