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KingGeorge
Group Title
[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.
 2 years ago
 2 years ago
KingGeorge Group Title
[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.
 2 years ago
 2 years ago

This Question is Closed

abb50 Group TitleBest ResponseYou've already chosen the best response.0
\[\sqrt {3 \times 3} \times 3\]
 2 years ago

abb50 Group TitleBest ResponseYou've already chosen the best response.0
\[3^0 \times 3 \times 3\]
 2 years ago

Cortegu10 Group TitleBest ResponseYou've already chosen the best response.0
\[\sqrt{3!3!3!}\]
 2 years ago

KingGeorge Group TitleBest 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 \(\sqrt{3!3!3!}=\sqrt{6^3}=6\sqrt{6}\neq9\)
 2 years ago

Cortegu10 Group TitleBest ResponseYou've already chosen the best response.0
oh damn i tried :)
 2 years ago

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

KingGeorge Group TitleBest 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.
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
\[ \sqrt{3!3!} + 3\]
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
\[ 3^{\frac{3!} 3}\]
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
Excellent once again!
 2 years ago

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

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
greatt!!!! sin3 works!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
perhaps log 3 too :D
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
sin3 is something between 0 and 1, so it will. cos3 unfortunately is negative.
 2 years ago

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
hmm.. the plus sign..
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
Ah great this works ceil 9^(cos(3))
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
\[ \lceil (3*3)^{\cos 3} \rceil \]
 2 years ago

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

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
@experimentX \[\sqrt{3!3!} \times 3\]..youarent allowed to use + lol
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
i mean \[\sqrt{3!3!} + 3\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
you cant use plus
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
Should've caught that :/
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
I have at least 4 more solutions no one has posted so far =D
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
\[ \left\lceil \sqrt[3]{\left( \sqrt{\left(3!3!\right)}\right)!}\right\rceil\]
 2 years ago

Ishaan94 Group TitleBest 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.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
\[ (3*3)^{\lfloor \sqrt 3\rfloor }\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
i bet sqrt 3 can be replaced with ln log using ceil ..
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
I still have 3 more solutions that look different from any posted above.
 2 years ago

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

experimentX Group TitleBest 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
 2 years ago

anonymoustwo44 Group TitleBest ResponseYou've already chosen the best response.0
e^(3ln(3))/3
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
How about \[\large 3^{\lceil\sqrt3\rceil\cdot\lfloor\sqrt3\rfloor}\]
 2 years ago

experimentX Group TitleBest 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
 2 years ago

KingGeorge Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
is e allowed??
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

experimentX Group TitleBest 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
 2 years ago

anonymoustwo44 Group TitleBest ResponseYou've already chosen the best response.0
33 (mod 3)
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
\(33\equiv0\pmod3\), although you have a case in that \(9\equiv0\pmod3\) as well.
 2 years ago

KingGeorge Group TitleBest 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.
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{3\times3!}{\Gamma(3)}=9\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.5
Nice idea
 2 years ago

KingGeorge Group TitleBest 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 \(^33=3^{3^3}=3^{27}\)
 2 years ago
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