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#1 2007-10-03 14:03:43

El
Guest

Problem Solving Algebraic Expressions

In the addition problems below, each letter is to represent the same digit in both problems.  Each letter is to be a digit 1 through 9, so that both addition problems are true.

  ABC
+DEF
--------
G H I


   ADG
+ BEH
---------
C F I



Thanks if you can help! El

#2 2007-10-03 16:01:03

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Problem Solving Algebraic Expressions

Each of these puzzles have a huge amount of solutions.  Start with defining C and F (in the first one), then find out what I is.  Then try to find what letters B and E are (they could be many different numbers), then find out what H is (remember you have to check if it carries).  Finally, do the same for the last column.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2007-10-03 17:39:57

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Problem Solving Algebraic Expressions

Here are some answers for you.  Enjoy!!
I had a blast programming this in the C language.

    A B C
    D E F  (format used below)
    G H I

    2 5 8
    4 7 1  (look thru from back lying on right side for other way)
    7 2 9

    4 3 8
    2 9 1
    7 2 9

    3 4 8
    2 9 1
    6 3 9

    1 5 7
    4 8 2
    6 3 9

    1 4 6
    5 8 3
    7 2 9

    7 2 9
    1 3 5
    8 6 4

    7 1 8
    2 3 6
    9 5 4

Last edited by John E. Franklin (2007-10-03 17:49:59)


igloo myrtilles fourmis

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#4 2007-10-03 18:21:33

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Problem Solving Algebraic Expressions

Wow John, are you a computer programmer by profession, or by hobby? You seem to be able to apply programming to nearly every maths question!

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#5 2007-10-04 02:48:59

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Problem Solving Algebraic Expressions

Thanks for the WOW, I started programming when my Dad bought me a Commodore Vic 20 with 4K of RAM.  It did BASIC, but I learned its machine code by hex numbers later on in a book.  That was around 1984.  So it all started by hobby, and I wrote lots of programs just by trial and error like your signature.  When I was a kid, once I woke up in the morning with a solution to how to pass the information around in my program.  Later in college I took Data Structures, an awesome course, but only got an AC for acceptable, which equals a B or C grade because the tests were limited in time to complete and you had to write algorithms in funny code the teacher made up.  Then I graduated with electrical engineering degree, but was not satisfied with my knowledge and found no jobs.  So I worked at a grocery store and then was a machine operator and finally I got a job as a C programmer temporary worker for Markem Corporation in Keene, NH, after I took a C course at Keene State College.  So then I worked 4 years there doing C, and then 3 years in Vermont doing C & Visual Basic.   Then I changed my lifestyle and lived in rural areas and hiked a lot and worked odd jobs while I fought off some personal paranoia that struck me in my thirties.   And now I still program as a hobby when something sparks my interest.


igloo myrtilles fourmis

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