1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?