Sum the squares cryptarithmetically, get square

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    Square Squares Sum
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Discussion Overview

The discussion revolves around solving a cryptarithmetic equation where participants are tasked with substituting letters with different decimal digits to satisfy the equation (PQR)² + (STUQ)² = (SVWX)². The challenge includes ensuring that each letter represents a unique digit and that neither P nor S can be zero.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant points out a typing error in the initial setup, noting that U = W = P = 1 violates the requirement for unique digits.
  • Another participant expresses confidence in resolving the ambiguity related to V = Q = 8, suggesting that further clarification is possible.
  • A later reply indicates difficulty in finding a solution that satisfies all unique digit constraints for PQRSTUVWX.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the solution, as there are multiple competing views regarding the validity of certain digit assignments and the overall solvability of the equation.

Contextual Notes

The discussion highlights limitations related to the uniqueness of digit assignments and the constraints imposed by the equation, but does not resolve these issues.

K Sengupta
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Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation:

(PQR)2 + (STUQ)2 = (SVWX)2

Note: None of P and S can be zero.
 
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(125)2 + (7812)2 = (7813)2
 
dsa said:
(125)2 + (7812)2 = (7813)2

There seems to be a minor typing error.

U = W = P = 1 contravenes the provision that each letter need to represent a different digit.
 
OK, this one is better:wink:

(480)2 + (1768)2 = (1832)2
 
dsa said:
OK, this one is better:wink:

(480)2 + (1768)2 = (1832)2

Very good, dsa.

I am now certain that you will be able to obviate the ambiguity corresponding to V=Q=8.
 
K Sengupta said:
Very good, dsa.

I am now certain that you will be able to obviate the ambiguity corresponding to V=Q=8.

I cannot find a solution for all unique PQRSTUVWX :frown:
 

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