Product equality and sum of squares equality puzzle

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SUMMARY

The forum discussion centers on a cryptarithmetic puzzle involving the equation ABCD * EF = GHJB * KE, along with the Pythagorean relationship (EH)² + (KC)² = (KH)². Participants emphasize the need for unique digit assignments for each letter, ensuring no leading zeros. The challenge lies in finding valid combinations that satisfy both the multiplication and the sum of squares conditions, requiring systematic trial and error or algorithmic approaches.

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  • Understanding of cryptarithmetic puzzles
  • Basic knowledge of algebra and number theory
  • Familiarity with Pythagorean triples
  • Experience with programming or algorithm design for solving combinatorial problems
NEXT STEPS
  • Explore techniques for solving cryptarithmetic puzzles using backtracking algorithms
  • Study the properties of Pythagorean triples and their applications
  • Learn about digit substitution methods in combinatorial mathematics
  • Investigate programming languages or tools like Python for implementing puzzle-solving algorithms
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Mathematicians, puzzle enthusiasts, computer scientists, and anyone interested in algorithmic problem-solving and cryptography.

K Sengupta
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Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero.

ABCD*EF=GHJB*KE, and:

(EH)2 + (KC)2 = (KH)2
 
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abcd*ef=ghjb*ke
9807*14=6538*21

(eh)2 + (kc)2 = (kh)2
(15)2 + (20)2 = (25)2
 

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