Question

A troll suddenly joins OpenStudy and he/she comes to know that a capital i and a lowercase L look the same. How many troll accounts can he/she make with them if the character limit is 10?
For example:
LiLLiLLLii
iLLLLLiiiL
LiL
Lii
LiiiLLL
etc.

Question 2: He/she comes to know that the 1st letter can't be L because all of them starting with an L are taken. What now?

Answer 1

pls report abuse for the troll if u see one :P

Answer 2

lol no it's a question

Answer 3

length has to be 10 ? or < 10 is also ok ?
he can create \[2^{10}\] unique accounts of 10 character length each

b. half of above

Answer 4

Yes, he can also create accounts with length of 9,8 and so on..

Answer 5

I guess the answer is pretty obvious from now.

Answer 6

Do you guys want the solution?

Answer 7

Hint: We'll add the combinations for different number of letters ^_^

Answer 8

\[\sum_{n=1}^{10} 2^{10}\]

Answer 9

\(\Large \sum_{k = 1} ^{10} 2^k\)
In Summation notation

Answer 10

Yeah exactly.

Answer 11

2(2^10-1)

Answer 12

Yeah, as we know, the answer to the second one would be half of that, so we can say:

\(\Huge \sum_{k = 1} ^{10} {2^{k} \over 2} = 2^0 + 2^1 +...2^9\)

Answer 13

@slaaibak thats much better... looks cute...

Answer 14

@AccessDenied when I type the same thing with equation editor, it comes out under the sigma, but when I type it out with hand, it's on the right of the sigma.

Answer 15

by hand*

Answer 16

Are you using parentheses when you type it out? ( )

Answer 17

By that I mean the actual in-line open/close tags

Answer 18

\(\Large\sum_{k = 1}\)

I'm using this \sum_{k = 1}^{10}

Answer 19

\[\sum_{n=1}^{10} 2^{10} = 2(2^{10}-1)\]

Answer 20

Yeah, inline

Answer 21

Oh yeah I got it

Answer 22

It doesn't work with the inline tags

Answer 23

Yeah, when you use in-line, it does that.
You have to use a command to fix that, I think its \limits?

Answer 24

Yeah, \sum \limits _{... } ^{... } and so on

Answer 25

Where else does the \limits command work?

Answer 26

\(\LARGE \sum \limits_{n = 1}^{10}2^n\)
I see. Works beautifully :D

Answer 27

\(\LARGE\prod \limits_{n = 1}^{10} 2^n \)

Works in the product one as well.

Answer 28

I believe whenever you have a situation with something being written on top / on bottom of text, it can work.
Like, \prod \limits, \lim \limits, and \int \limits

Answer 29

I see.

Answer 30

I love it xD

Answer 31

See all lol

Answer 32

<--- on the left