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Thread: Maths Puzzle- The 4 4's

  1. #1
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    Maths Puzzle- The 4 4's

    OK so here is a challenge that will certainly make you think.
    Can you make the numbers 0 to 20 by using just 4 lots of the number 4 in varying combinations?

    "But how?" You ask!

    You can use any of the following
    +
    -
    x
    /
    4
    .4
    44
    ^

    (that little ^ means "power of")

    No use of ! (factorial) or logs allowed.

    I'll give you an example to help you get it

    12= (4x(4-(4/4)))

    Sorry, I know it's hard to write maths stuff on here!

    The trickiest ones are 4,6,13,14,19

    There is more than one solution, I will post the answers in a day or so.

    Yours
    Mr Mathematics

    P.S. I hope someone else can solve this, it took me a little while to think on (I do have the answers)
    Last edited by joebeanyuk; 05-26-2003 at 01:46 PM.
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  2. #2
    http://www.flipshark.com flipshark's Avatar
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    This is kind of easy, just time consuming.

    1= (4/4)
    2= (4/4)+(4/4)
    3= (4 -(4/4))
    4= (4 X (4/4))
    5= (4 +(4/4))
    6= (4 + ((4/4)+(4/4)))
    Okay I'm bored so I'll just start doing the "hard ones"
    13= ((4X4) + (4/4)) - 4
    14= (4X4) - ((4/4) + (4/4))
    19= ((4X4)- (4/4)) + 4

  3. #3
    Loop Junkie calpomatt's Avatar
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    Well...looks like I'm bored since I actually tried this:

    0 = 4 + 4 - 4 - 4
    1 = (4/4)(44/44)
    2 = (4/4) + (44/44)
    3 = ((4x4) - 4)/4
    4 = ((44 - 4)/4)/4
    5 = ((4x4) + 4)/4
    6 = ((4x4)(.4)) - .4
    7 = (4 + 4) - (4/4)
    8 = ((4x4)/4) + 4
    9 = (4/.4) - (4/4)
    10 = (44/4) - (4/4)
    11 = (44/4)(4/4)
    12 = (44/4) + (4/4)
    13 =
    14 = (44x.4) + .4 - 4
    15 = (4x4) - (4/4)
    16 = ((44 - 4)/4) - 4
    17 = (4x4) + (4/4)
    18 = (4/.4) + 4 + 4
    19 = (44/4) + 4 + 4
    20 = ((44 - 4)/4) + 4

    I only had about 15 minutes to do these....I'll give #13 another shot when I get back from lunch.

  4. #4
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    Yeah but that's not using 4 lots of the number 4. You have used more or less than. In each case you have to use the number 4, 4 times. So chew on that one if you will

    OK I will give you another example
    19= (((4+4)-.4)/.4)

    That's how it supposed to be done, you see, four lots of four. Using the number 4, 4 times to make 19.
    He was just a normal man 'till this cheeky little hormone called testosterone kicked in
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  5. #5
    Loop Junkie calpomatt's Avatar
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    Originally posted by flipshark
    This is kind of easy, just time consuming.

    1= (4/4)
    2= (4/4)+(4/4)
    3= (4 -(4/4))
    4= (4 X (4/4))
    5= (4 +(4/4))
    6= (4 + ((4/4)+(4/4)))
    Okay I'm bored so I'll just start doing the "hard ones"
    13= ((4X4) + (4/4)) - 4
    14= (4X4) - ((4/4) + (4/4))
    19= ((4X4)- (4/4)) + 4
    I think the idea is that you have to use exactly four numbers...which makes it a lot tougher. Other wise you could just add (4/4) + (4/4)..... until you got them all

  6. #6
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    Originally posted by calpomatt
    Well...looks like I'm bored since I actually tried this:

    0 = 4 + 4 - 4 - 4
    1 = (4/4)(44/44)
    2 = (4/4) + (44/44)
    3 = ((4x4) - 4)/4
    4 = ((44 - 4)/4)/4
    5 = ((4x4) + 4)/4
    6 = ((4x4)(.4)) - .4
    7 = (4 + 4) - (4/4)
    8 = ((4x4)/4) + 4
    9 = (4/.4) - (4/4)
    10 = (44/4) - (4/4)
    11 = (44/4)(4/4)
    12 = (44/4) + (4/4)
    13 =
    14 = (44x.4) + .4 - 4
    15 = (4x4) - (4/4)
    16 = ((44 - 4)/4) - 4
    17 = (4x4) + (4/4)
    18 = (4/.4) + 4 + 4
    19 = (44/4) + 4 + 4
    20 = ((44 - 4)/4) + 4

    I only had about 15 minutes to do these....I'll give #13 another shot when I get back from lunch.
    OK the ones that are wrong are:
    1
    2
    4
    10
    11
    12
    13
    14
    16
    19
    20

    You did not use the number 4, 4 times, you just used 4 a lot of times to get what you wanted. You cannot use the number 4 more or less than 4 times to get any number. So have a bit more of a thinker on that
    He was just a normal man 'till this cheeky little hormone called testosterone kicked in
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  7. #7
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    Originally posted by calpomatt
    I think the idea is that you have to use exactly four numbers...which makes it a lot tougher. Other wise you could just add (4/4) + (4/4)..... until you got them all
    That is exactly right, heh someone gets it. Answers to be posted in about 12 hours time
    He was just a normal man 'till this cheeky little hormone called testosterone kicked in
    http://www.xtcf.com

  8. #8
    Loop Junkie calpomatt's Avatar
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    Ohhh....ok. I thought you were saying we were supposed to use 4, .4, and 44 exactly four times....not just the digit 4. Here it is with a few corrections:

    0 = 4 + 4 - 4 - 4
    1 = (4/4)(4/4)
    2 = (4/4) + (4/4)
    3 = ((4x4) - 4)/4
    4 = ?
    5 = ((4x4) + 4)/4
    6 = ((4x4)(.4)) - .4
    7 = (4 + 4) - (4/4)
    8 = ((4x4)/4) + 4
    9 = (4/.4) - (4/4)
    10 = (4/4)(4/.4)
    11 = ?
    12 = ?
    13 = ?
    14 = ((4 - .4)(4)) - .4
    15 = (4x4) - (4/4)
    16 = 4 + 4 + 4 +4
    17 = (4x4) + (4/4)
    18 = (4/.4) + 4 + 4
    19 = ((4+4)-.4)/.4
    20 = (4/.4) + (4/.4)

  9. #9
    Retired Mod aversion's Avatar
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    ones not gotten

    4 = 4x(4-4)+4
    11 = (44/(squareroot(4 * 4)))


    it took three people to come up with these

    edit - can I use square root?
    Last edited by aversion; 05-26-2003 at 08:05 PM.

  10. #10
    Loop Junkie calpomatt's Avatar
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    Originally posted by aversion
    4 = 4x(4-4)+4
    How did I not think of that! Must be a little slow after 3 days of wine tasting.

    No square roots though....just the symbols he wrote above.

  11. #11
    Retired Mod aversion's Avatar
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    well

    12 = (4+0.4+0.4)/0.4


    still stuck on 13 though


  12. #12
    BradyWhite.net Kac's Avatar
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    mmm... 13... let me think

    (4^4) = 256
    (4*4) = 16
    (4*.4) = 1.6
    (4/.4) = 10
    (4^.4) = 1.7411011265
    (4+4) = 8
    (4-.4) = 3.6
    (44^.4) = 4.543401013

    13 = well... (4-.4)*(4-.4) = 12.96 (if you round it = 13 ) ?? (I know its wrong but best I could do..

    11 = (4/.4)+(4/4)

    a few more ideas...
    (4*4)-.4 = 15.6 ... so if we *could* do this...
    (4*4)-.4-(4-.4) = 13

    hmmm...

  13. #13
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    Originally posted by aversion
    ones not gotten

    4 = 4x(4-4)+4
    11 = (44/(squareroot(4 * 4)))


    it took three people to come up with these

    edit - can I use square root?
    but you can use ^0.5 which is the same thing.


    *thinks*

    4^(4/(4+4))

    gives you two, but you ain't got no numbers left.


    i'm stuck on 11 and 13. annoying as..... a crying baby on a longhaul flight!!!

    edit: is 44 definately 2 uses of the number 4?

    //jgo
    Last edited by jgo; 05-27-2003 at 04:03 AM.
    jgo: pleased to meet you.

  14. #14
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    Well here are the answers

    0= (4-4)+(4-4)
    1= (4x4)/(4x4)
    2= (4/.4)-(4+4)
    3= ((4x4)-4)/4
    4= 4x(4^(4-4))
    5= ((4x4)+4)/4
    6= (4x.4)+(4+.4)
    7= (4+4)-(4/4)
    8= ((4x4)/4)+4
    9= (4+4)+(4/4)
    10= (4/.4)+(4-4)
    11= (4/.4)+(4/4)
    12= 4x(4-(4/4))
    13= ((4-.4)/.4)+4
    14= ((4x.4)+4)/.4
    15= (4x4)-(4/4)
    16= (4+4)+(4+4)
    17= (4x4)+(4/4)
    18= (4/.4)+(4+4)
    19= ((4+4)-.4)/.4
    20= (4/.4)+(4/.4)

    There is more than one solution to quite a few of these.
    By the way you can't use square root, as it's not technically 4. You can use 4th root, if you needed it. That means you can't have ^ unless it is ^4.4 ^4-4 etc

    Good attempts though, it did take a while to come up with 13.
    Last edited by joebeanyuk; 05-27-2003 at 04:13 AM.
    He was just a normal man 'till this cheeky little hormone called testosterone kicked in
    http://www.xtcf.com

  15. #15
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    Originally posted by joebeanyuk
    11= (4/.4)+(4/4)
    13= ((4-.4)/.4)+4
    now they just seem obvious!

    oh well - i didn't do too bad

    0 = (4+4)+(4-4)
    1 = 44/44
    2 = (4/4) + (4/4)
    3 = (4+4+4)/4
    4 = 4*(4^(4-4))
    5 = ((4*4)+4)/4
    6 = ((4*4)*0.4) - 0.4
    7 = (4+4)-(4/4)
    8 = (4*4)-(4+4)
    9 = (4/4)+4+4
    10 = (44-4)/4
    11 = ?
    12 = (44+4)/4
    13 = ?
    14 = ((4-.4)*4) - .4
    15 = (4*4)-(4/4)
    16 = 4+4+4+4
    17 = (4*4)+(4/4)
    18 = (44*0.4)+0.4
    19 = ((4+4)-.4)/.4
    20 = 4*(4+(4/4))

    //jgo
    jgo: pleased to meet you.

  16. #16
    BradyWhite.net Kac's Avatar
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    blast, I was soo close... 3.6 / .4 = 9!!! DAMG IT!

    at least I got 11 that makes me happy.

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