Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integer solutions for equations A * [(B + C)(D - E) - F(G*H) ] / J = 1

  1. Dec 26, 2007 #1
    Could anyone please answer this


    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.

    Thanks
     
  2. jcsd
  3. Dec 26, 2007 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You have 3 equations and 9 unknowns, so most likely, you have lots of solutions.

    Let us set A=J, H=3, G=0, whereby we must have (B+C)(D-E)=10

    Setting now B=2, C must be 3, and D-E=2.

    These particular choices determine 720 distinct solutions to your problem.

    Or should your numbers be non-repeating? (Your uniqueness condition?)

    Okay, I forgot that none of your numbers should be zero, either.

    Then your problem is difficult, in the sense of being tedious:
    If I have counted correctly, there exist 26 different quadruples (B,C,G,H) so that C-B=1, H-G=3, and all 4 numbers are unique, single digit numbers.

    You will solve your problem on a trial&error basis restricting yourself to these 26 special cases.
     
    Last edited: Dec 26, 2007
  4. Dec 26, 2007 #3
    Aw come on, I just want the answer in a hurry!

    It is Christmas, afer all.
     
  5. Dec 26, 2007 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, since there will exist for each such quadruple 10 combinations of D and E (since D-E must be positive), and the three remaining numbers can be placed in the A, J F positions, you are free to analyze the 26*10*6=1560 special cases occurring.

    But don't count upon us to do it for you.
     
  6. Dec 26, 2007 #5

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    Ben Fido, please read and follow the rules for these forums.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook