Thinking About Thinking

How Many Unique bit.ly Combinations Are There?

Posted in Pop Culture, Technology by larrycheng on August 16, 2010

I was thinking randomly about how many bit.ly combinations there are and how much unique shortened URLs they can generate given their current construct.  Here’s their construct:

  • Up to 6 characters after bit.ly/
  • Any mix of capitalized letters, lowercase letters, and numbers

If you limit the combinations to only ones where bit.ly is the domain (and not partner domains), and you presume they can go up to 6 characters (i.e. 1–6) as opposed to exactly 6 characters – how many total combinations are there?  Any math whiz out there who can figure it out pretty quickly and enlighten us in the comments section?  My small math brain was getting cramps thinking about it. 

Given that they shorten 40–50 million URLS per day, I also wonder how long they can last on this construct.  Probably a long time I suspect even including their growth.  Random thought for the day, and thanks for the help. 

Tags:

29 Responses

Subscribe to comments with RSS.

  1. Charlie Kroll said, on August 16, 2010 at 9:22 am

    57,731,386,986?

    • larrycheng said, on August 16, 2010 at 9:23 am

      Charlie – how’d you get to that answer? Sounds plausible.

  2. Charlie Kroll said, on August 16, 2010 at 9:29 am

    Assumptions were…
    * 62 possible characters (26 letters, each can be upper or lower case, plus 10 numerical characters).
    * String can be 1-6 characters long

    So, calculation would be (62^6)+(62^5)+(62^4)+(62^3)+(62^2)+(62^1)

    Make sense?

    • Dave Gordon said, on August 16, 2010 at 10:12 am

      I think the answer is actually slightly different. This is a permutations problem requiring the formula n!/(n-k)! where “n” is the set of values you are choosing from (in this case the number of possible characters) and “k” is the length of the string. Using 62 possible characters and strings of 6, 5, 4, 3, 2, 1 your formula would be:

      62!/(56!) + 62!/(57!) + 62!/(58!) + 62!/(59!) + 62!/(60!) + 62!/(51!) =

      45,051,792,964 possible permutations

      • Dave Gordon said, on August 16, 2010 at 10:15 am

        actually nevermind, this would assume the use of each value only once, which in a bit.ly url isnt a requirement – so charlie’s answer is right. in any case, now you know how to solve for permutations!

  3. SuggestionBox.com said, on August 16, 2010 at 10:28 am

    Thanks for asking! I have always wondered the same thing, and keep waiting for the day they extend to 7 characters.

    FYI: All bit.ly links use the same shortened URL regardless of “partner domains”

    The shortened link for this post is:

    http://bit.ly/c2Sp5a
    http://j.mp/c2Sp5a
    http://bitly.com/c2Sp5a

    A post from TechCrunch this am is:
    http://tcrn.ch/aa4WRS
    http://bit.ly/aa4WRS
    http://j.mp/aa4WRS
    http://bitly.com/aa4WRS

    However, you can’t hijack someone else’s shortened URL and try to make it your own:
    http://tcrn.ch/c2Sp5a

    Another consideration is custom domains longer than 6 characters like:

    http://j.mp/HowManyUniquebitlyCombinationsAreThere

  4. Hemang said, on August 16, 2010 at 10:32 am

    I do believe Charlie has the right answer. The breakout is as follows:

    62^6= 56800235584
    62^5= 916132832
    62^4= 14776336
    62^3= 238328
    62^2= 3844
    62^1= 62

    Total = 57,731,386,986

    • Hemang said, on August 16, 2010 at 10:35 am

      Just to clarify Larry, 62^6 represents the number of combos if you could ONLY have 6 characters. So you take the total combos for each number of characters possible and that should be the right number.

  5. larrycheng said, on August 16, 2010 at 10:17 pm

    Thanks all – sounds like we have a consensus!

  6. Desmond Pieri said, on August 18, 2010 at 5:48 pm

    Thanks for figuring this out guys. I wasn’t able to sleep nights recently, worrying if I was using up more than my fair share of bit.lys. Now I can rest assured. Des

  7. Julien Nakache said, on August 20, 2010 at 11:27 am

    The math behind that are so trivial that I don’t understand the point of this article. Was that a way to get some comments on your blog ?

    Idea for a next blog post : now that we know how many different urls bit.ly can generate and the fact they are shortening 50million links a day, how long will they be able to shorten urls ? Seems complicated…

    Sorry for being sarcastic, but seriously, it s VERY basic math…

    • larrycheng said, on October 5, 2010 at 4:38 pm

      Julien and Marco – I guess I’m just a mere math mortal. I can live with that!

  8. Marco Gomes said, on August 24, 2010 at 11:49 pm

    I am brazilian, brazilian education is made for monkeys, and even I knew the answer for this math question :)

    (I am brazilian, I can make jokes with brazilian educational system :)

  9. Dave Rodecker said, on September 28, 2010 at 1:07 am

    Extra credit assignment:
    If in the new land of IPv6, there exists a need to create unique IPs for each bit.ly URL.
    So, if the entire scope of about 62^6 bit.ly URLs were mapped to IPv6 addresses, what is the minimum IPv6 subnet that could contain it?

  10. Athman Mohamed said, on December 25, 2010 at 3:09 pm

    Interesting thought. I had another one, I once typed in http://bit.ly into bit.ly and it gave me this: http://bit.ly/QtQET

    is THAT shortening? LoL :D

  11. Andrew said, on January 3, 2011 at 6:19 pm

    26 letters, upper and lower case, plus 0-9 = 72 unique characters, right?

    72^6 = 139,314,069,504

  12. J.S. said, on January 5, 2011 at 6:09 am

    @andrew
    26 + 26 + 10 = 62

    I wondered that bit ly’s don’t give URL’s that vary from 1 to 6 strings; they are always exactly 6 strings
    So, the number should be
    62 ^ 6 = 56, 800, 235, 584
    Correct me if im wrong, but I never saw a bit ly less than 6 characters.

  13. barry said, on March 23, 2011 at 6:23 am

    Which surely means bit.ly will run out in about 3 years. (50 thousand million @ 50 million per day = 1000 days = 3 years all approximations).So time to add an extra character?

  14. Drew said, on March 28, 2011 at 9:26 pm

    If they upped it to 8 characters then it would be 62^8 = 2.18340106 × 10^14

    Considering IPv4 allows 32 bits for an Internet Protocol address, and can therefore support 2^32 (4,294,967,296) addresses, IPv6 uses 128-bit addresses, so the new address space supports 2^128 (approximately 340 undecillion or 3.4×10^38) addresses.

  15. rinnai water heaters said, on September 14, 2013 at 5:40 am

    I khow this iif off topic but I’m looking into starting my own blog
    and was wondering what all is required to get set up?
    I’m aswsuming having a blog like yours would cost a pretty
    penny? I’m not very internet smart so I’m not 100% certain.
    Any tips or advice would be greatly appreciated.
    Cheers

  16. How To Drain A Rheem Water Heater said, on September 14, 2013 at 6:55 am

    Hello colleagues, how is all, and what you desire to say
    concerning this paragraph, in mmy view its truly amazinng ddesigned
    for me.

  17. bridal shoes said, on September 18, 2013 at 4:11 pm

    I ggot this web psge from my pal whho informed me concerning this web
    site and at the moment thi time Iam browsing this website and reading very informative articles or reviews at this place.

  18. Tankless Heater Reviews said, on September 20, 2013 at 3:07 am

    I got this web site from my pal who informedd me regarding this
    web page and now this time I am browsing this site and reading very informative content
    at this place.

  19. Jacques said, on October 4, 2013 at 3:59 am

    I’m no longer sure where you are getting your info, but great topic.
    I needs to spend some time finding out much more or figuring out more.
    Thanks for magnificent information I used to be on the
    lookout for this information for my mission.

  20. Sam Woods said, on March 26, 2014 at 5:54 am

    That’s a lot of possible shortened links! must be highly optimized to handle that. They’re also adding other small domains arn’t they?

  21. Buzznet.com said, on March 31, 2014 at 9:52 am

    Finally, the 2010 study shows that behavior toward direct
    mail is what you call center operations manager job description need,when you get the disk though.
    So if you want more robust analysis, there iss a need
    to remind or update people with new offerings in mailing schemes,
    such as the location in which they live, age group, education, location, etc.
    If it doesn’t, it hasn’t call center operations manager job description done its job.
    With regularly direct mail, and online printing.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 88 other followers

%d bloggers like this: