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KingGeorge

  • 3 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: \(-(-\sqrt{3^3\cdot3})\), \(-(-3-3-3)\) and similar don't count.

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  1. abb50
    • 3 years ago
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    \[\sqrt {3 \times 3} \times 3\]

  2. abb50
    • 3 years ago
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    \[3^0 \times 3 \times 3\]

  3. Cortegu10
    • 3 years ago
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    \[\sqrt{3!3!3!}\]

  4. KingGeorge
    • 3 years ago
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    @abb50 That has a 0 in it. Let me correct the problem to specify against that. @Cortegu10 \(\sqrt{3!3!3!}=\sqrt{6^3}=6\sqrt{6}\neq9\)

  5. Cortegu10
    • 3 years ago
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    oh damn i tried :)

  6. UnkleRhaukus
    • 3 years ago
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    this probably dosent count as there are four 3's best i can do \[3 \log_3(3)^3=9\]

  7. KingGeorge
    • 3 years ago
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    Too many 3's there :( Nice try though. I know of at least 3 more expressions using increasingly convoluted nested functions.

  8. KingGeorge
    • 3 years ago
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    Hint (for a couple): Keep thinking with factorials and exponents. And remember, "-" isn't completely ruled out. Just don't abuse it.

  9. experimentX
    • 3 years ago
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    \[ \sqrt{3!3!} + 3\]

  10. KingGeorge
    • 3 years ago
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    Excellent. I hadn't thought that one. Also, feel free to abuse the floor and ceiling function.

  11. experimentX
    • 3 years ago
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    \[ 3^{\frac{3!} 3}\]

  12. KingGeorge
    • 3 years ago
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    Excellent once again!

  13. experimentX
    • 3 years ago
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    LOL .. not sure if it works \[ \left \lfloor {3*3 + \sin 3} \right \rfloor \] \[ \left \lceil {3*3 + \cos 3} \right \rceil \]

  14. apoorvk
    • 3 years ago
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    greatt!!!! sin3 works!!

  15. experimentX
    • 3 years ago
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    perhaps log 3 too :D

  16. KingGeorge
    • 3 years ago
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    If you could do those without the "+" sign, those would be accepted. I'm pretty sure you can get rid of it however.

  17. apoorvk
    • 3 years ago
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    sin3 is something between 0 and 1, so it will. cos3 unfortunately is negative.

  18. apoorvk
    • 3 years ago
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    hmm.. the plus sign..

  19. KingGeorge
    • 3 years ago
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    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.

  20. experimentX
    • 3 years ago
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    Ah great this works ceil 9^(-cos(3))

  21. experimentX
    • 3 years ago
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    \[ \lceil (3*3)^{-\cos 3} \rceil \]

  22. KingGeorge
    • 3 years ago
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    This is probably the most convoluted solution I've come up with \[\left\lceil \sqrt[3]{\left(\left(\lfloor\sqrt3\rfloor3\right)!\right)!}\right\rceil\]

  23. lgbasallote
    • 3 years ago
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    @experimentX \[\sqrt{3!3!} \times 3\]..youarent allowed to use + lol

  24. lgbasallote
    • 3 years ago
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    i mean \[\sqrt{3!3!} + 3\]

  25. lgbasallote
    • 3 years ago
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    you cant use plus

  26. KingGeorge
    • 3 years ago
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    Should've caught that :/

  27. KingGeorge
    • 3 years ago
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    I have at least 4 more solutions no one has posted so far =D

  28. experimentX
    • 3 years ago
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    \[ \left\lceil \sqrt[3]{\left( \sqrt{\left(3!3!\right)}\right)!}\right\rceil\]

  29. Ishaan94
    • 3 years ago
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    \[y=\left(\frac{x^3}{3}\right)\]dy/dx at x=3 lol but it's identical to (3^3)/3. Not sure if it counts.

  30. experimentX
    • 3 years ago
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    \[ (3*3)^{\lfloor \sqrt 3\rfloor }\]

  31. experimentX
    • 3 years ago
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    i bet sqrt 3 can be replaced with ln log using ceil ..

  32. KingGeorge
    • 3 years ago
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    Probably, but let's try and get things that look new, and not just replacing one part with another.

  33. KingGeorge
    • 3 years ago
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    I still have 3 more solutions that look different from any posted above.

  34. experimentX
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=3%5Eceil%28log%5B10%2C+3%5E3%5D%29

  35. experimentX
    • 3 years ago
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    lol ... this ceil function is so useful http://www.wolframalpha.com/input/?i=3%5Eceil%28+sqrt%283*ln+3%29%5D%29

  36. anonymoustwo44
    • 3 years ago
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    e^(3ln(3))/3

  37. KingGeorge
    • 3 years ago
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    How about \[\large 3^{\lceil\sqrt3\rceil\cdot\lfloor\sqrt3\rfloor}\]

  38. experimentX
    • 3 years ago
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    lol ... i think we should ban usage of ceil http://www.wolframalpha.com/input/?i=3*+ceil%28log+%283*3%29%29

  39. KingGeorge
    • 3 years ago
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    Alright. Let's ban the ceiling function for now. What else have we got? btw, I still have 2 more different solutions

  40. experimentX
    • 3 years ago
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    is e allowed??

  41. KingGeorge
    • 3 years ago
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    Let's restrict it so we don't have \(e\), \(\pi\), \(\phi\), or other constants like that for now.

  42. KingGeorge
    • 3 years ago
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    Also, let's stay out of integrals and derivatives for now as well. Maybe I'll do this again with those allowed.

  43. experimentX
    • 3 years ago
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    this seem to have interesting result http://www.wolframalpha.com/input/?i=floor%28ln%28%283*3%29%21%29+-+3%29

  44. anonymoustwo44
    • 3 years ago
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    33 (mod 3)

  45. KingGeorge
    • 3 years ago
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    \(33\equiv0\pmod3\), although you have a case in that \(9\equiv0\pmod3\) as well.

  46. KingGeorge
    • 3 years ago
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    I've got to go to bed now. Keep posting solutions, and I'll post the ones I have left tomorrow.

  47. UnkleRhaukus
    • 3 years ago
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    \[\frac{3\times3!}{\Gamma(3)}=9\]

  48. experimentX
    • 3 years ago
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    Nice idea

  49. KingGeorge
    • 3 years ago
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    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 \(^33=3^{3^3}=3^{27}\)

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