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Math Help - I am stucked by this question

  1. #1
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    I am stucked by this question

    Is it possible to complete the following expression

    2 **** 9 = 2009

    and make it true by replacing the asterisks with a selection of the four operational symbols (+ - x / ) and the two other asterisks with digits 0,1,2....,9? Operational symbols and digits can be the same.


    Thank you
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  2. #2
    Newbie drichie's Avatar
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    What about 2+3*669
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  3. #3
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    I am stuck with this question

    Hi Drichie,

    Sorry, there are 3 digits and 2 operator in your answer unfortunately. Please try again.
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  4. #4
    Newbie drichie's Avatar
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    2018-9
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  5. #5
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    I am stucked with this question

    Hi Driche,

    Thank you for your reply again, but unfortunately, your answer has 3 digit and 1 operator and it still cannot meet the conditions of the question asked. i.e. 2 operator and 2 digits only.
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  6. #6
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    how about 2 x 10 cubic+9 =2009
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  7. #7
    Senior Member I-Think's Avatar
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    2 cents

    I'd like to throw in my 2cents and look at this in a case by case basis, if I correctly understand the question.

    You want to complete the expression 2****9=2009, using two digits from 0-9 and two operational symbols from (+,-,x,/).
    Two operational symbols cannot go together, so I'll break this into 3 cases.
    ( D=Digit, S=Symbol)

    Case 1
    2DSDS9=2009

    If the final S is a x, the equation is not viable as 2DSD can only produce an integer, while 2009/9=223.22....
    If it is a +, that would require 2DSD=2000, not going to happen.
    If it is a -, 2DSD=2018, ditto.
    If it is a /, 2DSD=18081
    Case 1 is will not work.

    Case 2
    2SDDS9=2009
    If final S is a x, the same result as Case 1
    If it is a +, then 2SDD=2000, same as Case 1
    If it's a -,same result as Case 1
    If it's a /, same result as Case 1
    Case 2 will not work.

    Case 3
    2SDSD9=2009
    If final S is a x, then the final D must be a 4, as 49 is a factor of 2009.
    Then 2SD=41, not going to happen
    If it is a +, then 2SD=2009-D9. The RHS can be at the least 1910, while the LHS can be at most 18, this won't work.
    If it is a -, then, then it won't work again because of the same reason as the +.
    If it's a /, it won't work just like the previous cases.
    Case 3 will not work

    As these are all the possible cases, I conclude that there is no solution to this question.

    This is my line of reasoning and I could be wrong, so try to get a second opinion.
    If exponents are allowed, then glen's solution would be correct, though it seems they aren't allowed.

    Btw, who gave you get this question?
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