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 2 years 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.
 2 years 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Just 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.

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

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

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

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

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

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

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

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

Ishaan94
 2 years ago
Best 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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