How to Solve a Logic Problem with Numbers Using Equations?

  • Thread starter Thread starter mhill
  • Start date Start date
  • Tags Tags
    Logic Numbers
Click For Summary

Homework Help Overview

The discussion revolves around a logic problem involving a four-digit number represented as ABCD and another number CDAB. The relationship between these numbers is defined by the equation 2 × (ABCD) = CDAB - 5. Participants are attempting to determine the values of A, B, C, and D based on this equation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty in their attempts to solve the problem, with one mentioning brute force methods yielding incongruences. Another suggests breaking down the numbers into powers of ten to clarify their values. There is also a mention of reformulating the problem into a Diophantine equation, which raises questions about finding integer solutions.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have provided guidance on how to reformulate the problem, while others are questioning the nature of the solutions and the methods used. There is no explicit consensus on the best approach yet.

Contextual Notes

Participants note the constraints of the problem, including the requirement for A, B, C, and D to be digits and the implications of the equation leading to potentially infinite integer solutions. There is also a reference to a similar previous thread, indicating a shared context in problem-solving approaches.

mhill
Messages
180
Reaction score
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
 
Physics news on Phys.org
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"
 
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.
 
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.
 
This looks quite similar to https://www.physicsforums.com/showthread.php?t=230969 by the way.
 
Very similar! That's why I deleted that thread.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
1
Views
2K
Replies
4
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 20 ·
Replies
20
Views
3K
  • · Replies 21 ·
Replies
21
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K