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Thread: A mixed bunch

  1. #1
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    A mixed bunch

    1) The number is secret, it has 3 digits.
    a) The sum of the 3 digits multiplied by 36 equals the secret number
    [img]/forums/images/smilies/cool.gif[/img] If you multiply the first digit by 7 and then add 9 you will get the same as the sum of the two other digits multiplied by 5.
    c) If you multiply the second digit with 8 and then take away 9 you will get the same number as the sum of the first and third digits.

    What is the secret number?

    2) 48 is a special number.

    a) If you add 1 to it you get a square (7x7=49)
    [img]/forums/images/smilies/cool.gif[/img] If you add 1 to half of 48 you get 25 which is also a square (5x5=25)

    What is the next number which this rule applies?

    3) After you burn a candle, you get a stub. By using 6 stubs, you can make a candle. You have 1001 stubs, how many new candles can you make?
    Jerry

  2. #2
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    Re: A mixed bunch

    2. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1680: 1681 = 41*41 and 841 = 29*29.</span hide>

  3. #3
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    Re: A mixed bunch

    3. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">200:
    Use 996 stubs to make 166 candles; 5 stubs left over.
    Burn the 166 candles. You now have 166+5 = 171 stubs.
    Use 168 stubs to make 28 candles; 3 stubs left over.
    Burn the 28 candles. You now have 28+3 = 31 stubs.
    Use 30 stubs to make 5 candles; 1 stub left over.
    Burn the 5 candles. You now have 5+1 = 6 stubs.
    Use the 6 stubs to make 1 candle.
    (If you burn the last one, you have just one stub. Not enough to make more candles.)
    Total made: 166+28+5+1 = 200.</span hide>

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    Re: A mixed bunch

    Well done Hans 2 and 3 correct
    Jerry

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    Re: A mixed bunch

    1. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">324

    9*(3+2+4) = 9*36 = 324
    7*3+9 = (2+4)*5
    8*2-9 = 3+4</span hide>

  6. #6
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    Re: A mixed bunch

    Well done again.

    My scratch pad got a good scribbling on this morning!
    Jerry

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    Re: A mixed bunch

    OK Hans

    What is the next one.
    Jerry

  8. #8
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    Re: A mixed bunch

    The next ones are <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">57120, 1940448 and 65918160.</span hide>

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    Re: A mixed bunch

    I doff my cap to you sir.

    I did it in Excel, what was your secret, scratch pad or VB?
    Jerry

  10. #10
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    Re: A mixed bunch

    I solved 1 and 3 with pen and paper, and used a VBA macro to solve 2 (it happened to be in Excel, but it could have been any application with VBA).

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    Re: A mixed bunch

    I tried to have a go at 2. using diophantine equations (which I know very little about). Such an equation would be of the form:
    y

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