What is the solution to this equation involving cats, dogs, and lambs?

  • Context: High School 
  • Thread starter Thread starter Bad_Boy_Blue
  • Start date Start date
Click For Summary
SUMMARY

The equation "cats + dogs = lamb" presents a problem that can be interpreted as a cryptarithm, where each letter represents a unique digit. Participants in the discussion highlight the complexity of solving this equation without computational assistance, noting that it involves ten different letters, which must each correspond to a unique digit. Simplifying the equation by moving "cats" to the other side yields "dogs = lamb - cats," but the challenge remains in determining the specific values for each letter. The consensus is that a program may be necessary to explore the numerous possibilities effectively.

PREREQUISITES
  • Understanding of cryptarithms and their properties
  • Familiarity with basic algebraic manipulation
  • Knowledge of programming for computational problem-solving
  • Experience with combinatorial logic and digit assignments
NEXT STEPS
  • Explore cryptarithm solving techniques using Python
  • Learn about backtracking algorithms for combinatorial problems
  • Investigate the use of constraint satisfaction problems in programming
  • Study digit assignment strategies in mathematical puzzles
USEFUL FOR

Mathematicians, computer scientists, puzzle enthusiasts, and educators looking to enhance problem-solving skills in cryptarithms and computational logic.

Bad_Boy_Blue
Messages
7
Reaction score
0
If cats + dogs = lamb, what does dogs equal?
 
Mathematics news on Phys.org
Please simplify your answers as I'm finding this concept rather difficult to get my head around.
 
Bad_Boy_Blue said:
If cats + dogs = lamb, what does dogs equal?
Surely you just move the cats to the other side of the equals sign. Right?

The Bob (2004 ©)
 
Is this a problem where every letter is assigned a digit? And thus this problem is the sum of two four digit numbers? Or is it something else entirely?

- Warren
 
If it is what chroot is suggesting it is, it looks hard to figure without using a computer. Making a few simple eliminations (O=0 or 9), reduces the number of possibilities to about 10^5 - notice that there are 10 different letters, so all the digits must be used. Hmmm...looks like a toughie.

Are you just making up a generic example off the top of your head, or is this the exact question from a book or homework ? If the former, there may be no solution at all, and even if there are solutions, they may not be paper-and-pencil-able.

Are you allowed to write a program ?
 
Last edited:

Similar threads

Why cats are smarter than dogs
  • · Replies 41 ·
2
Replies
41
Views
7K
Constant acceleration problem: Dog chasing a surprised cat
  • · Replies 13 ·
Replies
13
Views
1K
High School What Defines a 2-Way Frequency Table?
  • · Replies 7 ·
Replies
7
Views
2K
Why are dogs more intelligent than cats?
  • · Replies 38 ·
2
Replies
38
Views
6K
High School Schrödingers cat, is it just mumbo-jumbo?
  • · Replies 39 ·
2
Replies
39
Views
4K
Undergrad Why don't we bury Schrodinger's Cat?
  • · Replies 143 ·
5
Replies
143
Views
11K
High School Does Schrödinger's Cat Know Its Own Fate?
  • · Replies 17 ·
Replies
17
Views
2K
High School New solutions to old, historic problems
  • · Replies 2 ·
Replies
2
Views
2K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Can a Cat Catch a Mouse Running in a Circle at the Same Speed?
  • · Replies 13 ·
Replies
13
Views
2K