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Homework Help: Really big formula

  1. Dec 3, 2006 #1
    You are confronted with the following formula:

    A * [(B + C)(D - E) - F(G*H) ] / J = 10

    Knowing that each variable is a unique, single-digit, nonzero number, and that C - B = 1, and H - G = 3, what is the number ABCDEFGHJ, where each letter is a digit? For example, if A = 4, B = 2, and C = 7, ABC would equal 427.

    I tried to set up some rwalsionship but I cannot elimante enough variblies to move on with the proplem. can anyone help please.
     
  2. jcsd
  3. Dec 3, 2006 #2
    This would be easy to solve by computer. There is a very finite list of numbers to check.
     
  4. Dec 3, 2006 #3
    Haha I like your teacher. This is my kind of problem. Give me a moment.
     
  5. Dec 3, 2006 #4
    Right off the bat it tells you C - B = 1. This tells you something about C + B. In particular it tells you C + B = odd number. This becomes very important as you are asked to multiply (B + C) (D - E).
     
  6. Dec 3, 2006 #5
    Actually I guess it's not that important. But if you seperate the equation to be:

    (A/J) * [(B + C)(D - E) - F(G*H) ] = 10

    This tells you A/J either = 2 or = 5, as there is no way to get a fraction from what's left. Now we know A/J must = 2. Because in order for A/J to = 5, A must be 10 and J must be 2. This violates our condition that all letters are single digits.

    And there are only a few possibilities for A/J. 4/2, 6/3, or 8/4.
     
  7. Dec 3, 2006 #6
    Ok I guess it is important that B + C is odd afterall.

    We have an equation H - G = 3. This tells us H - G is odd. Because either H must be odd and G even, or H must be even and G odd. An odd number * an even number gives an even number. So GH is an even number, likewise FGH must be an even number.

    This tells us (B+C)(D-E) must be odd, because (B + C)(D - E) - F(G*H) = 5.
     
  8. Dec 3, 2006 #7
    A = 6, J = 3.
     
  9. Dec 3, 2006 #8
    Ok I lied. A could also be = 2, and J = 1.
     
  10. Dec 4, 2006 #9
    i am still not understanding where you want be to go from here. I realize what you are talking about with the odd numbers. How do i figure out which numbers are the correct ones to use. with A and j having 3 different possiblies
     
  11. Dec 5, 2006 #10
    anyone else know anything else?
     
  12. Dec 6, 2006 #11
    The reason you didn't get a straight answer is because you didn't copy the problem down correctly.

    A * [(B + C)^(D - E) - F^(G*H) ] / J = 10

    they were exponents not products. I've seen this problem before is how I know.

    now you can get the right answer:

    256973148
     
    Last edited: Dec 6, 2006
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