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[SOLVED] Let's see some creativity!
Without using "+" make the number 9 using only three 3's, and no other digits using any mathematical symbol you want. So "3+3+3=9" and similar expressions are off limits.
Here are a couple of the examples I've found so far: \[\frac{3^3}{3}\]\[\sqrt{3^3\cdot3}\]I know of several more possibilities (not including various possible applications of negation). Which ones can you get?
PS: \((\sqrt{3^3\cdot3})\), \((333)\) and similar don't count.
 one year ago
 one year ago
[SOLVED] Let's see some creativity! Without using "+" make the number 9 using only three 3's, and no other digits using any mathematical symbol you want. So "3+3+3=9" and similar expressions are off limits. Here are a couple of the examples I've found so far: \[\frac{3^3}{3}\]\[\sqrt{3^3\cdot3}\]I know of several more possibilities (not including various possible applications of negation). Which ones can you get? PS: \((\sqrt{3^3\cdot3})\), \((333)\) and similar don't count.
 one year ago
 one year ago

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abb50Best ResponseYou've already chosen the best response.0
\[\sqrt {3 \times 3} \times 3\]
 one year ago

abb50Best ResponseYou've already chosen the best response.0
\[3^0 \times 3 \times 3\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
@abb50 That has a 0 in it. Let me correct the problem to specify against that. @Cortegu10 \(\sqrt{3!3!3!}=\sqrt{6^3}=6\sqrt{6}\neq9\)
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
this probably dosent count as there are four 3's best i can do \[3 \log_3(3)^3=9\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Too many 3's there :( Nice try though. I know of at least 3 more expressions using increasingly convoluted nested functions.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Hint (for a couple): Keep thinking with factorials and exponents. And remember, "" isn't completely ruled out. Just don't abuse it.
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
\[ \sqrt{3!3!} + 3\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Excellent. I hadn't thought that one. Also, feel free to abuse the floor and ceiling function.
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
\[ 3^{\frac{3!} 3}\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Excellent once again!
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
LOL .. not sure if it works \[ \left \lfloor {3*3 + \sin 3} \right \rfloor \] \[ \left \lceil {3*3 + \cos 3} \right \rceil \]
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
greatt!!!! sin3 works!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
perhaps log 3 too :D
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
If you could do those without the "+" sign, those would be accepted. I'm pretty sure you can get rid of it however.
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
sin3 is something between 0 and 1, so it will. cos3 unfortunately is negative.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Just to be clear, (Partial) list of lesser known functions I will accept: \[\lfloor9.5=9\rfloor\]\[\lceil8.5=9\rceil\]\[^33=3^{3^3}\] Also, I will accept \(\ln\) for \(\log_e\) and \(\log\) for \(\log_{10}\) as allowable functions.
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
Ah great this works ceil 9^(cos(3))
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
\[ \lceil (3*3)^{\cos 3} \rceil \]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
This is probably the most convoluted solution I've come up with \[\left\lceil \sqrt[3]{\left(\left(\lfloor\sqrt3\rfloor3\right)!\right)!}\right\rceil\]
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
@experimentX \[\sqrt{3!3!} \times 3\]..youarent allowed to use + lol
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
i mean \[\sqrt{3!3!} + 3\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Should've caught that :/
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
I have at least 4 more solutions no one has posted so far =D
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
\[ \left\lceil \sqrt[3]{\left( \sqrt{\left(3!3!\right)}\right)!}\right\rceil\]
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
\[y=\left(\frac{x^3}{3}\right)\]dy/dx at x=3 lol but it's identical to (3^3)/3. Not sure if it counts.
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
\[ (3*3)^{\lfloor \sqrt 3\rfloor }\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
i bet sqrt 3 can be replaced with ln log using ceil ..
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Probably, but let's try and get things that look new, and not just replacing one part with another.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
I still have 3 more solutions that look different from any posted above.
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
http://www.wolframalpha.com/input/?i=3%5Eceil%28log%5B10%2C+3%5E3%5D%29
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
lol ... this ceil function is so useful http://www.wolframalpha.com/input/?i=3%5Eceil%28+sqrt%283*ln+3%29%5D%29
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
How about \[\large 3^{\lceil\sqrt3\rceil\cdot\lfloor\sqrt3\rfloor}\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
lol ... i think we should ban usage of ceil http://www.wolframalpha.com/input/?i=3*+ceil%28log+%283*3%29%29
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Alright. Let's ban the ceiling function for now. What else have we got? btw, I still have 2 more different solutions
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Let's restrict it so we don't have \(e\), \(\pi\), \(\phi\), or other constants like that for now.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Also, let's stay out of integrals and derivatives for now as well. Maybe I'll do this again with those allowed.
 one year ago

experimentXBest ResponseYou've already chosen the best response.5
this seem to have interesting result http://www.wolframalpha.com/input/?i=floor%28ln%28%283*3%29%21%29++3%29
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
\(33\equiv0\pmod3\), although you have a case in that \(9\equiv0\pmod3\) as well.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
I've got to go to bed now. Keep posting solutions, and I'll post the ones I have left tomorrow.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\frac{3\times3!}{\Gamma(3)}=9\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Here are the other ideas I've had that look different (mostly) from previous answers\[3^{3!}(3!)!\]\[\lfloor \log(^33))\rfloor3\]Recall that \(^33=3^{3^3}=3^{27}\)
 one year ago
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