KingGeorge
  • KingGeorge
[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: \(-(-\sqrt{3^3\cdot3})\), \(-(-3-3-3)\) and similar don't count.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\sqrt {3 \times 3} \times 3\]
anonymous
  • anonymous
\[3^0 \times 3 \times 3\]
anonymous
  • anonymous
\[\sqrt{3!3!3!}\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

KingGeorge
  • KingGeorge
@abb50 That has a 0 in it. Let me correct the problem to specify against that. @Cortegu10 \(\sqrt{3!3!3!}=\sqrt{6^3}=6\sqrt{6}\neq9\)
anonymous
  • anonymous
oh damn i tried :)
UnkleRhaukus
  • UnkleRhaukus
this probably dosent count as there are four 3's best i can do \[3 \log_3(3)^3=9\]
KingGeorge
  • KingGeorge
Too many 3's there :( Nice try though. I know of at least 3 more expressions using increasingly convoluted nested functions.
KingGeorge
  • KingGeorge
Hint (for a couple): Keep thinking with factorials and exponents. And remember, "-" isn't completely ruled out. Just don't abuse it.
experimentX
  • experimentX
\[ \sqrt{3!3!} + 3\]
KingGeorge
  • KingGeorge
Excellent. I hadn't thought that one. Also, feel free to abuse the floor and ceiling function.
experimentX
  • experimentX
\[ 3^{\frac{3!} 3}\]
KingGeorge
  • KingGeorge
Excellent once again!
experimentX
  • experimentX
LOL .. not sure if it works \[ \left \lfloor {3*3 + \sin 3} \right \rfloor \] \[ \left \lceil {3*3 + \cos 3} \right \rceil \]
apoorvk
  • apoorvk
greatt!!!! sin3 works!!
experimentX
  • experimentX
perhaps log 3 too :D
KingGeorge
  • KingGeorge
If you could do those without the "+" sign, those would be accepted. I'm pretty sure you can get rid of it however.
apoorvk
  • apoorvk
sin3 is something between 0 and 1, so it will. cos3 unfortunately is negative.
apoorvk
  • apoorvk
hmm.. the plus sign..
KingGeorge
  • KingGeorge
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.
experimentX
  • experimentX
Ah great this works ceil 9^(-cos(3))
experimentX
  • experimentX
\[ \lceil (3*3)^{-\cos 3} \rceil \]
KingGeorge
  • KingGeorge
This is probably the most convoluted solution I've come up with \[\left\lceil \sqrt[3]{\left(\left(\lfloor\sqrt3\rfloor3\right)!\right)!}\right\rceil\]
lgbasallote
  • lgbasallote
@experimentX \[\sqrt{3!3!} \times 3\]..youarent allowed to use + lol
lgbasallote
  • lgbasallote
i mean \[\sqrt{3!3!} + 3\]
lgbasallote
  • lgbasallote
you cant use plus
KingGeorge
  • KingGeorge
Should've caught that :/
KingGeorge
  • KingGeorge
I have at least 4 more solutions no one has posted so far =D
experimentX
  • experimentX
\[ \left\lceil \sqrt[3]{\left( \sqrt{\left(3!3!\right)}\right)!}\right\rceil\]
anonymous
  • anonymous
\[y=\left(\frac{x^3}{3}\right)\]dy/dx at x=3 lol but it's identical to (3^3)/3. Not sure if it counts.
experimentX
  • experimentX
\[ (3*3)^{\lfloor \sqrt 3\rfloor }\]
experimentX
  • experimentX
i bet sqrt 3 can be replaced with ln log using ceil ..
KingGeorge
  • KingGeorge
Probably, but let's try and get things that look new, and not just replacing one part with another.
KingGeorge
  • KingGeorge
I still have 3 more solutions that look different from any posted above.
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=3%5Eceil%28log%5B10%2C+3%5E3%5D%29
experimentX
  • experimentX
lol ... this ceil function is so useful http://www.wolframalpha.com/input/?i=3%5Eceil%28+sqrt%283*ln+3%29%5D%29
anonymous
  • anonymous
e^(3ln(3))/3
KingGeorge
  • KingGeorge
How about \[\large 3^{\lceil\sqrt3\rceil\cdot\lfloor\sqrt3\rfloor}\]
experimentX
  • experimentX
lol ... i think we should ban usage of ceil http://www.wolframalpha.com/input/?i=3*+ceil%28log+%283*3%29%29
KingGeorge
  • KingGeorge
Alright. Let's ban the ceiling function for now. What else have we got? btw, I still have 2 more different solutions
experimentX
  • experimentX
is e allowed??
KingGeorge
  • KingGeorge
Let's restrict it so we don't have \(e\), \(\pi\), \(\phi\), or other constants like that for now.
KingGeorge
  • KingGeorge
Also, let's stay out of integrals and derivatives for now as well. Maybe I'll do this again with those allowed.
experimentX
  • experimentX
this seem to have interesting result http://www.wolframalpha.com/input/?i=floor%28ln%28%283*3%29%21%29+-+3%29
anonymous
  • anonymous
33 (mod 3)
KingGeorge
  • KingGeorge
\(33\equiv0\pmod3\), although you have a case in that \(9\equiv0\pmod3\) as well.
KingGeorge
  • KingGeorge
I've got to go to bed now. Keep posting solutions, and I'll post the ones I have left tomorrow.
UnkleRhaukus
  • UnkleRhaukus
\[\frac{3\times3!}{\Gamma(3)}=9\]
experimentX
  • experimentX
Nice idea
KingGeorge
  • KingGeorge
Here are the other ideas I've had that look different (mostly) from previous answers\[3^{3!}-(3!)!\]\[\lfloor \log(^33))\rfloor-3\]Recall that \(^33=3^{3^3}=3^{27}\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.