How to Solve a Logic Problem with Numbers Using Equations?

Please don't post the same question more than once!In summary, when given two four-cipher numbers, ABCD and CDAB, such that 2x(ABCD) = CDAB - 5, the values of A, B, C, and D can be found by solving the Diophantine equation -199X+ 98Y= 5, where X = AB and Y = CD. This equation has an infinite number of integer solutions, but only one that gives two-digit positive integers for both X and Y.
  • #1
mhill
189
1

Homework Statement



given a number of four ciphers ABCD and another four cipher number CDAB get the values of A,B,C,D if we know that 2x (ABCD)=CDAB-5

Homework Equations



2X (ABCD)=CDAB-5

The Attempt at a Solution



no idea.. i have try by brute force but got no results only incongruences , for example B=-3 or similar here '2 x' means multiplication
 
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  • #2
You need to be a bit more elegant about this. Split it into powers of ten... for example in the ABCD cipher, the "A" is 100 times more value than the "A"
 
  • #3
no way , i get weird responses such us A=c=0 and B=-5/3 how are these kind of problems solved in Number theory ?? thanks.
 
  • #4
mhill said:

Homework Statement



given a number of four ciphers ABCD and another four cipher number CDAB get the values of A,B,C,D if we know that 2x (ABCD)=CDAB-5

Homework Equations



2X (ABCD)=CDAB-5

The Attempt at a Solution



no idea.. i have try by brute force but got no results only incongruences , for example B=-3 or similar here '2 x' means multiplication
Notice that AB and CD always appear together. I would do it this way:

Let X= AB and Y= CD. Then the equation says 2(100X+ Y)= 100Y+ X- 5. Combining the X and Y terms we get the Diophantine equation
-199X+ 98Y= 5. Do you know how to solve that? It has an infinite number of integer solutions but only one that gives a two digit positive integer for both X and Y.
 
  • #5
This looks quite similar to https://www.physicsforums.com/showthread.php?t=230969 by the way.
 
  • #6
Very similar! That's why I deleted that thread.
 

What is a logic problem of numbers?

A logic problem of numbers is a type of mathematical puzzle that requires critical thinking and analytical skills to solve. It typically involves a set of clues and a grid or chart to organize and eliminate possibilities until the correct solution is found.

How do you solve a logic problem of numbers?

To solve a logic problem of numbers, you must carefully read and analyze the given clues. Then, use deductive reasoning to eliminate possibilities and narrow down the potential solutions. It may also be helpful to chart out the information and use process of elimination to determine the correct answer.

What skills are needed to solve a logic problem of numbers?

Solving a logic problem of numbers requires critical thinking, deductive reasoning, and analytical skills. It also helps to have a good understanding of basic math concepts and the ability to organize information in a systematic way.

Are there any tips for solving a logic problem of numbers?

Yes, there are several tips that can help you solve a logic problem of numbers more efficiently. These include carefully reading and re-reading the clues, keeping track of eliminated possibilities, and using process of elimination to narrow down the potential solutions. It is also important to stay organized and approach the problem systematically.

Can logic problems of numbers have more than one solution?

Yes, it is possible for a logic problem of numbers to have multiple solutions. However, a well-designed problem should have only one correct solution. If you encounter a problem with multiple solutions, it is important to carefully review the clues and make sure your solution meets all of the given criteria.

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