Technique for solving numerical cryptograms?

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SUMMARY

The discussion centers on solving numerical cryptograms, specifically the example involving the words SEND, MORE, and MONEY. Participants suggest using systems of equations to represent the problem mathematically, but acknowledge that it results in an underdetermined system that lacks sufficient equations for a unique solution. The conversation highlights the potential of computational algorithms to verify guessed numbers quickly, indicating that an algorithmic approach is the most effective method for solving these types of puzzles.

PREREQUISITES
  • Understanding of systems of equations
  • Familiarity with underdetermined systems in mathematics
  • Basic knowledge of computational algorithms
  • Experience with numerical problem-solving techniques
NEXT STEPS
  • Research algorithms for solving constraint satisfaction problems
  • Explore methods for generating and verifying solutions in numerical puzzles
  • Learn about the application of backtracking algorithms in cryptographic problems
  • Investigate the use of programming languages like Python for implementing solution-checking algorithms
USEFUL FOR

Mathematicians, puzzle enthusiasts, computer scientists, and anyone interested in algorithmic problem-solving techniques for numerical cryptograms.

DyslexicHobo
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I'm sure everyone here has seen one of these things some time or another. Where you're given something like...

SEND
+MORE
______
MONEY

...and then you have to figure out what each letter represents as a number in order to make the solution make sense, and no two letters can equal the same number, and no number in front can equal zero.


This particular gram that I posted I already know the answer for, but is there a specific way to solve these?

I was thinking about using a systems of equations somehow, maybe...

1000s + 100e + 10n + d + 1000m + 100o + 10r + e = 10000m + 1000o + 100n + 10e + y.

... however I'm not sure how I'd get enough other equations to substitute!

There's got to be an easy, mathematical way to do these. Anyone got some ideas?
 
Mathematics news on Phys.org
Mathematically you get an underdetermined system of equations which cannot be solved.
Computationally this is an example for a TM with oracle band, i.e. guessed numbers can be verified quickly.

Considering nowadays possibilities, an algorithm which checks solutions would be the method of choice.
 

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