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Math Help - novice needs help

  1. #1
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    novice needs help

    I am needing help with the following six puzzles. Any and all help would be greatly appreciated.

    1. Here is a long division sum, showing all the work, and the result. Simple, right? The sum works out exactly, with no remainder. The slight complication is, that all the numbers have been replaced with letters on a random basis. However, one letter always represents the same number. Can you reconstruct the original sum?

    (The problem is ADGAAHD divided by AB) (CDEFG is the answer)

    ______CDEFG_________________

    AB ADGAAHD
    AJK
    -------------------------------------------
    AKA
    AAG
    ---------------------------------------------
    FA
    JF
    ------------------------------------------------
    AGH
    AEE
    --------------------------------------------------
    FD



    2. 6-2
    18


    8-7
    84

    12-4
    ?


    3. Can you figure out the reasoning of these numbers, and replace the question mark with the correct number?

    5 3 8 7
    12 15 49 56
    3 9 4 12
    18 27 36 ?


    4.Take a look at these digital "watches". By cracking the logic that connects them, you should be able to figure out what time should be on watch number five.


    15.14.01
    12.18.00
    08.26.58
    03.42.55
    ??.??.??


    5.Thirty-six

    Sixty-four

    Seventy-two

    Twenty-five

    Eighty-one

    What is the odd number out?



    6. Can you figure out the logic behind these number "squares" and find the number that replaces the question mark?

    9 6 5 10 4 6 ? 5
    4 2 3 7 8 11 12 7

    (Think of each set of four numbers as a square. 9 = top left, 4 = bottom left, 6 = top right, 2 = bottom right, and so on, it might help to write them down.)



    Thank you again for any and all help

    mathguy
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  2. #2
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    Hello, mathguy9!

    I hope I interpreted #1 correctly . . .


    1. Here is a long division sum, showing all the work, and the result.
    The divison works out exactly with no remainder.
    All the digits have been replaced with letters on a random basis.
    However, one letter always represents the same number.
    Can you reconstruct the original division?

    . . \begin{array}{cccccccccc}<br />
& & & & & C & D & E & F & G \\<br />
& & & -- & -- & -- & -- & -- & -- & -- \\<br />
A & B & | & A & D & G & A & A & H & D \\<br />
& & & A & J & K \\<br />
& & & -- & -- & -- \\<br />
& & & & A & K & A \\<br />
& & & & A & A & G \\<br />
& & & & -- & -- & -- \\<br />
& & & & & & F & A \\<br />
& & & & & & J & F \\<br />
& & & & & & -- & -- \\ \end{array}
    . . . . . . . . . . . . . . . . . . . . . \begin{array}{cccccccccc}<br />
& & & & & & A & G & H \\<br />
& & & & & & A & E & E \\<br />
& & & & & & -- & -- & -- \\<br />
& & & & & & & & F & D \\<br />
& & & & & & & & F & D \\<br />
& & & & & & & & -- & --<br />
\end{array}

    . . \begin{array}{ccc}<br />
A\:=\:1 & & F \:=\:7 \\<br />
B \:=\:9 && G \:=\:4 \\<br />
C\:=\:8 && H\:=\:0 \\<br />
D\:=\:6 && J\:=\:5 \\<br />
 E\:=\:3 && K\:=\: 2 \end{array}


    . . \begin{array}{cccccccccc}<br />
& & & & & 8 & 6 & 3 & 7 & 4 \\<br />
& & & -- & -- & -- & -- & -- & -- & -- \\<br />
1 & 9 & | & 1 & 6 & 4 & 1 & 1 & 0 & 6 \\<br />
& & & 1 & 5 & 2 \\<br />
& & & -- & -- & -- \\<br />
& & & & 1 & 2 & 1 \\<br />
& & & & 1 & 1 & 4 \\<br />
& & & & -- & -- & -- \\<br />
& & & & & & 7 & 1 \\<br />
& & & & & & 5 & 7 \\<br />
& & & & & & -- & -- \\ \end{array}
    . . . . . . . . . . . . . . . . . . . . . \begin{array}{cccccccccc}<br />
& & & & & & 1 & 4 & 0 \\<br />
& & & & & & 1 & 3 & 3 \\<br />
& & & & & & -- & -- & -- \\<br />
& & & & & & & & 7 & 6 \\<br />
& & & & & & & & 7 & 6 \\<br />
& & & & & & & & -- & --<br />
\end{array}

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  3. #3
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    Quote Originally Posted by mathguy9 View Post
    5.Thirty-six
    Sixty-four
    Seventy-two
    Twenty-five
    Eighty-one
    What is the odd number out?
    Question really means: which number does not belong ?
    Easy...LOOK carefully!
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  4. #4
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    Hello, mathguy9!

    I think I have #4 . . .


    4. Take a look at these digital "watches".
    By cracking the logic that connects them, you should be able
    to figure out what time should be on watch number five.

    . . \begin{array}{ccccc}\text{H} && \text{M} && \text{S} \\ \hline<br />
 15 & : & 14 & : & 01 \\<br />
12 & : & 18 & : & 00 \\<br />
08 & : & 26 & : & 58 \\<br />
03 & : & 42 &:& 55 \\<br />
? &:& ? &:& ? \end{array}

    The consecutive differences of the Hours suggest this sequence:

    . \begin{array}{c|ccccccccc}\text{Hours} & 15 && 12 && 8 && 3 && {\color{blue}\text{-}3} \\ \hline<br />
\text{Difference} &&  \text{-}3 && \text{-}4 && \text{-}5 && {\color{blue}\text{-}6} \end{array}


    The consecutive differences of the Minutes suggest this sequence:

    . \begin{array}{c|ccccccccc}\text{Minutes} & 14 && 18 && 26 && 42 && {\color{blue}74} \\ \hline<br />
\text{Difference} &&  +4 && +8 && +16 && {\color{blue}+32} \end{array}


    The consecutive differences of the Seconds suggest this sequence:

    . \begin{array}{c|ccccccccc}\text{Seconds} & 01 && 00 && 58 && 55 && {\color{blue}51} \\ \hline<br />
\text{Difference} &&  \text{-}1 && \text{-}2 && \text{-}3 && {\color{blue}\text{-}4} \end{array}


    \begin{array}{cccccccc}\text{The final time is:} & -3 & : & 74 &:& 51 \\<br />
\text{which convets to:} & 09 &:& 74 &:& 51 \\<br /> <br />
\text{and finally:} & 10 &:& 14 &:& 51 \end{array}



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  5. #5
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    3. Can you figure out the reasoning of these numbers, and replace the question mark with the correct number?

    5 3 8 7
    12 15 49 56
    3 9 4 12
    18 27 36 ?


    The answer is 48. The numbers are in four squares of four numbers, so the first square is:

    5 3 let this be: a b
    12 15 c d

    You will find that in each square, c = (a-1)*b and d=a*b.

    In the final square, 4*12=48
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  6. #6
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    you guys are so great. Thank you so much for all your help.
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  7. #7
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    For the sixth question

    The answer is 9.

    Here's the pattern:

    6*4 - 2*9 = 24 - 18 = 6
    10*3 - 7*5 = 30 - 35 = -5
    6*8 - 4*11 = 48 - 44 = 4
    5*12 - 7*9 = 60 - 63 = -3

    To caution, patterns are useful but sometimes more than one pattern can match up with the problem at hand so keep a sharp eye open for that.
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  8. #8
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    Hello, mathguy9!

    I have five answers to problem #5.


    5. . \begin{array}{c}\text{Thirty-six} \\ <br />
\text{Sixty-four} \\ \text{Seventy-two} \\ \text{Twenty-five} \\ \text{Eighty-one} \end{array} . . What is the odd number out?

    36 - the only number with 9 divisors.

    64 - the only number whose sum of digits is even.

    72 - the only number which is not a square.

    25 - the only number less than 33.

    81 - the only number greater than 77.

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