How Can You Solve for 33 Using Only Four 4s?

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To solve for 33 using four 4s, consider incorporating decimals and various mathematical operations. Resources like Wikipedia and dedicated websites provide extensive information on the four fours challenge. Users have found success in solving similar problems through personal exploration and online searches. It's advised to verify any current solutions to ensure accuracy. Engaging with these resources can enhance understanding and enjoyment of the challenge.
UNknown 2010
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Hi All :smile:,

Can you help me in this game ?

Use four fours ONLY to get numbers from 0 to 100

I need help in 33

http://img528.imageshack.us/img528/1480/gametm8.png​
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I don't know what 33 is, but it looks like your #5 equals 20.
 
They have entire portions of websites dedicated to this. Most of them are common sense - for my class years ago, we had the option of doing this for extra credit and I found almost all of them by myself (and somewhat enjoyed it). If you really get stuck, though, I recommend Wikipedia (http://en.wikipedia.org/wiki/Four_fours) and just searching Google, which almost always yields results (i.e. http://www.dwheeler.com/fourfours/fourfours.txt).
 
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If you don't want just answers - for #33, remember that you can also use decimals in your equations.

I'd double check your current answers, too.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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