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Math Help - Logic

  1. #1
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    Logic

    we have to fill out the ??? with digits.
    **********

    Bagels: no digit is correct
    pico: one digit is correct, but in the wrong position
    fermi: one digit is correct and in the correct position

    1)
    1 2 3 -- bagels
    4 5 6 -- pico
    7 8 9 -- pico
    0 7 5 -- pico fermi
    0 8 7 -- pico
    ? ? ?

    2)
    9 0 8 -- bagels
    1 3 4 -- pico
    3 8 7 -- pico fermi
    2 5 6 -- fermi
    2 3 7 -- pico fermi
    ? ? ?

    *********

    for #1, i tried to make a chart to eliminate which number it could be. i got 905 as the answer for #1 but i'm not sure. i just have no idea how to begin. thanks in advance for the help.
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  2. #2
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    i got 273 for #2... but i think there possibly might be 2 answers for this question. the other answer probably begins with 2 and ends with 7. i don't know...
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  3. #3
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    I doubt that you will get a response to this problem.
    It is not because we do not want to help; but it is that we dont understand.
    This is what is known as a special knowledge question.
    Unless you give us a complete set of definitions, I doubt you can expect an answer.
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  4. #4
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    In my view, these are not logic problems as much as they are organization problems.

    You DO have to draw a map. Some folks can see it in their heads. If you are not one of those, write it down. Let's assume you get the data sequentially.

    Without any information, except the assumption that no digit can appear twice, there are 10*9*8 = 720 possibilities

    1 2 3 -- bagels

    This is the best possible first response!! (Well, excepting the low probability event of getting it right from a random attack.) We can just throw out these three digits. There are noe 7*6*5 = 210 possibilities.

    4 5 7 - 1 but not in the right place

    This gives 6 forms. It must be

    ?? 4 ??
    ?? ?? 4
    5 ?? ??
    ?? ?? 5
    7 ?? ??
    ?? 7 ??

    This leaves only 6*(1*6*5) = 180 possibilities. Really, this is a very slight improvement - a disappointing result.

    7 8 9 - 1 but not in the right place.

    ?? 7 ??
    ?? ?? 7
    8 ?? ??
    ?? ?? 8
    9 ?? ??
    ?? 9 ??

    It is now substantially difficult to count the remaining possibilities. I'm sure we have eliminated some, but I cannot see how to judge how many. This is a very disappointing result and the main reason why I never would start such a game with these first three moves. Using all different numbers every time doesn't give enough information. From the previous guess, one of them is correct. You should start testing theories! Anyway...

    0 7 5 -- 2 but only 1 in the right place.

    Aha! This is a GREAT response. The possibilities are now very few.

    Assume 0 is right
    0 5 ??
    0 ?? 7
    Assume 7 is right
    5 7 ??
    ?? 7 0
    Assume 5 is right
    7 ?? 5
    ?? 0 5

    All right, that's enough of that. I never want to do that again.

    Is there another way to proceed? Maybe, but like I said, organization is the trick.
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  5. #5
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    Quote Originally Posted by trancefanatic View Post
    we have to fill out the ??? with digits.
    **********

    Bagels: no digit is correct
    pico: one digit is correct, but in the wrong position
    fermi: one digit is correct and in the correct position

    1)
    1 2 3 -- bagels
    4 5 6 -- pico
    7 8 9 -- pico
    0 7 5 -- pico fermi
    0 8 7 -- pico
    ? ? ?

    2)
    9 0 8 -- bagels
    1 3 4 -- pico
    3 8 7 -- pico fermi
    2 5 6 -- fermi
    2 3 7 -- pico fermi
    ? ? ?

    *********

    for #1, i tried to make a chart to eliminate which number it could be. i got 905 as the answer for #1 but i'm not sure. i just have no idea how to begin. thanks in advance for the help.
    Pico, Fermi, Bagels!

    Oh, I remember thise game from Discrete Math. Boy its been a while. By using the laws stated (I'm assuming they are Bagels: no digit is correct; Pico: one digit is correct, but in the wrong position; Fermi: one digit is correct and in the correct position, you have to determine the correct string of digits.

    I'll help you with the first:

    1)
    1 2 3 -- bagels
    4 5 6 -- pico
    7 8 9 -- pico
    0 7 5 -- pico fermi
    0 8 7 -- pico
    ? ? ?

    So you can instantly eliminate 1, 2, 3.
    From 4, 5, 6, one is correct, and the other 2 you can eliminate.
    For 7, 8, 9, one is correct, and the other 2 you can eliminate. This forces 0 to be one of the correct digits (do you see why?).

    Looking at 0, 7, 5 -> 0, 8, 7, you lose a "fermi" but retain a pico. We can deduce that 5 was the correct digit from the list 4, 5, 6. From the list 7, 8, 9, we can eliminate 7 and 8. Thus the correct digit from that list is 9.

    And thus, the correct sequence is: 7 0 5

    You should be able to go from here.
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