Having trouble solving this....

Discussion in 'Physics & Math' started by Xenia, Mar 27, 2003.

  1. Xenia Registered Member

    Messages:
    3
    Hi, have been lurking here at sciforums for quite a while... all you guys are pretty cool. Well, I'm playing a game and I can't seem to decifer or solve the problem. Thought you guys could help... please?

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    It's a times table. and it's not in order. Each letter is a number but it's not in chronological order. There are 10 letters.

    The letters are: A-G-H-K-L-N-S-U-X-Y


    The problems are:

    X*U=AK
    X*S=NH
    X*G=X
    X*GY=XY
    X*H=AG
    X*GG=XX
    X*K=LN
    X*N=UA
    X*GA=KU
    X*L=HL
    X*A=GU
    X*X=US

    Can you guys help? Can't seem to get my thinking cap on this one.... It's probably very easy but I just don't get it. btw, the game is all in good fun, no real winners, or prizes or such. It's just for the sake of having fun.
     
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  3. HallsofIvy Registered Senior Member

    Messages:
    307
    (Technically, you mean to say that each letter represents a DIGIT and they are not in numerical order. Also I am assuming although you did not say it that each letter is a DISTINCT digit.)

    I don't know that I will be able to do it all just sitting here but
    one obvious point is that "X*G=X" tells us that G= 1.

    Then from "X*GY= XY" we know X*1Y= 10X+XY= XY So we must have XY= Y. Since neither X nor Y can be 1 we must have Y= 0 so that X*1Y= X*10= X0. Of course, X*GG= XX just confirms that G= 1: X*11= XX.

    Looking at "X*L= HL", just try things: L can't be 2 because then it would have to be 6*2= 12 and H can't be 1. L can't be 3 because X*3 doesn't end in a "3" for any X>1. L COULD be 4 because 6*4= 24. L could also be 5 (in which case X cpuld be 7 or 9).

    I'll let others take it from here. I have to run.
     
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  5. slimshady2357 Registered Member

    Messages:
    20
    Dammit, I'm supposed to be working

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    But I couldn't help looking at this.

    X*G=X, so G =1

    And From X*GA=KU and X*A=GU

    You can get 1) X*1A=KU and 2)X*A =1U

    NOTE: I am assuming that when you write KU you mean a two digit number, first number K second number U. NOT K times U

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    1) is also 10X + X*A = KU

    Subtract 2) and you get

    10X = KU - 1U

    Now if you look at KU - 1U and think about it, you'll see that it must be (k-1)0 (that is, the first digit is (k-1) and the second digit is zero)

    Since say, 27 - 17 = 10 (k =2, U= 7) or 49 -19 = 30 (k=4, U=9)
    Get it?

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    Therefore you have

    10X = (k-1)0

    And therefore X = K-1

    That's all I have for now

    G =1 and X = K -1
    But it should help you start.


    Adam
     
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  7. slimshady2357 Registered Member

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    Just to be clear, what he means is:

    X*GY = XY

    Therefore X*1Y = 10X + X*Y = XY

    And that XY can be written as 10X + Y

    Therefore, 10X +X*Y = 10X + Y

    And therefor X*Y = Y

    And, since G =1, therefore Y = 0

    It gets hard to read if you leave out the * when you mean multiplication

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    So you now have X= K - 1 and G = 1 and Y = 0

    Adam
     
  8. slimshady2357 Registered Member

    Messages:
    20
    Ok, solved the rest

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    The key, after you know G =1 is this equation.

    X*H = AG

    Since G =1, the AG is either 11, 21, 31,..., 91. Out of these, only 21 can be the product of 2 single digit numbers. And those numbers are 3 and 7.

    And that gives A = 2

    Now, either X = 3 or X =7

    But we have X*A = GU

    or X*2 = 1U

    But 3*2 is only 6, so X must be 7.

    That gives X=7, G=1, Y=0, A=2, U=4 (from 7*2 = 1U)

    The rest are easy.... that was fun

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    Adam
     
  9. Xenia Registered Member

    Messages:
    3
    Thank you!! Thank you!! You guys are the best.

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    And Andre,

    Questions + Answers = Appreciation.

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    The answers were easy though I just couldn't see it yesterday... Kudos to everyone. This is very much appreciated.

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