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Posers and Puzzles

Posers and Puzzles

  1. 08 Mar '08 19:25 / 2 edits
    I was just watching a local adoption of the show "Are you smarter than a 5thgrader?" and there was an old lady playing. She struggled to answer a question "Find a way to express 10 with five 9". While she figured out 99/ 9 - 9/9 = 10, I figured out 14 more ways to do it?

    How many ways can you guys find?

    P.s. I used derivatives, trigonometry, logarithms. There definitely are more ways, but the number I gave is how many I found during the question.
  2. 08 Mar '08 19:47 / 1 edit
    Originally posted by kbaumen
    I was just watching a local adoption of the show "Are you smarter than a 5thgrader?" and there was an old lady playing. She struggled to answer a question "Find a way to express 10 with five 9". While she figured out (99 - 9) - 9/9 = 10, I figured out 14 more ways to do it?

    How many ways can you guys find?

    P.s. I used derivatives, trigonometry, logarit ...[text shortened]... ere definitely are more ways, but the number I gave is how many I found during the question.
    the old lady lost didn't she?
    Because she found a way to express 89 inted of 10:
    (99-9)-9/9=90-1=89 !!!
    here's a easy one : 99/99 + 9
  3. 08 Mar '08 19:55
    Originally posted by alexdino
    the old lady lost didn't she?
    Because she found a way to express 89 inted of 10:
    (99-9)-9/9=90-1=89 !!!
    here's a easy one : 99/99 + 9
    Ooops, sorry, my mistake. Fixed now.
  4. 08 Mar '08 20:50
    some easy ones off the top of my head:

    1. 9-9+9+(9/9)
    2.(9/9)^99 + 9
    3. 9-9+9+log(9-9)
    4. 9-9+9+[log(base 9) of 9]
    5. 9/9+[9th root of 9^9)

    etc. if you allow the use of log base 9, 9th power and 9th root to achieve a value of 1, you can find tons and tons

    i wonder how well 5 9s could be used to write the set of whole numbers, a la the classic four 4s problem? intriguing..
  5. 08 Mar '08 21:19 / 1 edit
    I'll post some others I found:

    sin9sin9 + cos9cos9 + 9 = 10
    (99 - 9)/9 + derivative(9) = 10 (I suppose if you derive a constant function, hence a constant number, the derivative is 0)
    (tg9ctg9 + 9) * 9 / 9 = 10

    Eh, yeah, there really are tons of possibilities.

    Ok, let's make 1 to 100 with five 9. (with only + - * /, hence no trigonometry, logarithmic expressions, calculus, combinatorics and other creepy stuff)

    I'll start:

    1 = (99 - 9) / 9 - 9
  6. 08 Mar '08 21:30 / 1 edit
    2 = 9/9+(9/9)^9
    3 = (9+9)/9 + 9/9
  7. 08 Mar '08 21:35
    4 = (9+9+9+9)/9
  8. 08 Mar '08 21:53 / 2 edits
    5 = sqrt(9) + 9/9 + 9/9

    EDIT: Damn, I didn't mention square root. Ah, consider it an option. I think some numbers will be quite hard to get without sqrt. However, no sqr(9), hence 9^2, please.
  9. 09 Mar '08 00:10
    6 = (9/9)^9 * (9 - sqrt(9))
    numbers not so close to multiples of 9 are a bit more dificult so i thinc that without sqrt you can't get them wiith only 5 9s.
    but you can always try!
    7 = 9 - 9/9- 9/9
  10. 09 Mar '08 06:19
    8 = 9-9+9-9/9
  11. 09 Mar '08 06:35
    9 = (9*9)-(9*9) + 9
  12. 09 Mar '08 09:29
    As already posted 10 = 99/99 + 9

    11 = 9 + 9/9 + 9/9
  13. 09 Mar '08 15:13
    12 = (9+9+9)/9 + 9
    13 = 9 + sqrt(9) + (9+9)/9
    14 = 9 +9 - sqrt(9) - 9/9
    15 = (9 - sqrt(9) + 9) * 9/9
  14. 09 Mar '08 16:51 / 2 edits
    Originally posted by alexdino

    13 = 9 + sqrt(9) + (9+9)/9
    Check this one (above) again.

    16 = 9 + 9 - sqrt(9) + 9/9
  15. 09 Mar '08 17:40
    ooopps
    13 = 9 + sqrt(9) + (9/9)^9