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Three 3's

  1. Nov 16, 2005 #1
    I know this is old, but let's see how many fall for it here.

    a) What is the largest number you can make using three 9's?

    b) What is the largest number you can make using three 3's?

    Operations allowed are addition, subtaction, multiplication, division and exponentiation.
  2. jcsd
  3. Nov 16, 2005 #2
    Hmm, maybe:

    Last edited: Nov 16, 2005
  4. Nov 16, 2005 #3
    Maybe :

    . 3 / (3-3)

    Figured with your comment " how many fall for it "
    there must be a trick - was this it??
    Last edited: Nov 17, 2005
  5. Nov 17, 2005 #4
    or maybe:
    or something along those lines.

    How do I make it invisible?

    Last edited: Nov 17, 2005
  6. Nov 17, 2005 #5
    None of the pre-set colors match the new skin, but if you use e9e9e9 it'll be invisible. I.e. <bracket>color="#e9e9e9"<bracket> Text <bracket>/color<bracket> (not sure how to make a bracket actually show up instead of being interpreted). Demo: Invisible text
  7. Nov 17, 2005 #6
    new white out code

    See 11-15-2005 post in "sticky thread" at top of Brain teaser forum

    for new white out code to macth new skin.
    Testing here for e9e9e9 maybe it works too
    Test of e9 above -- either black or e9e9e9 seems work ok
    Last edited: Nov 17, 2005
  8. Nov 18, 2005 #7
    I see you fell for it

    a) The answer is 9^(9^9).

    b) The answer is 3^33. You should see that this is greater than 3^(3^3), which is 3^27.

    That was the trick.

    As far as I know 3/(3-3) is not defined as 3/0 is not defined, since the left hand and right hand limits are not equal.
  9. Nov 18, 2005 #8
    Sorry about not seeing the sticky at the time. I picked e9e9e9 by simply checking what the background rendered to, though with color profiles, websafeness and what not it may well be something else when it starts out (I just hit printscreen, tabbed over to photoshop, pasted in a screenshot and looked) and/or be rendered as something else elsewhere. Not like 4/256 shade diff is gonna kill anyone anyhow :-).
  10. Nov 19, 2005 #9


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    I'm sorry, how did you get 33 from two 3s when all you can do is add, divide, multiply, subtract, and exponentiate? I call BS. You should have listed concatenate.

    (Although I did go over a few different ways fo fitting 9s together to get weird shapes...)
  11. Nov 19, 2005 #10


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    Rotate one 3 over 90 deg and the other one over -90 deg and stick them on top of each other to make [itex]\infty[/itex].
  12. Nov 25, 2005 #11
    so it means we only need two 3's instead of three???
  13. Nov 25, 2005 #12
    You could use the other one to make

  14. Dec 18, 2005 #13
    My bid is:
    Though my grasp of transfinite numbers is shakey at best, I think it's bigger then "infinity" (i.e. plain omega) and 3^infinity :-).
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