Sum the squares cryptarithmetically, get square

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The discussion revolves around solving a cryptarithmetic equation where each letter represents a different decimal digit from 0 to 9. The equation is structured as (PQR)² + (STUQ)² = (SVWX)², with the stipulation that neither P nor S can be zero. Participants note a minor typing error and highlight that assigning the same digit to multiple letters, such as U, W, and P all being 1, violates the unique digit requirement. There is a focus on resolving ambiguities in the assignment of digits, particularly with V and Q both being 8. Despite efforts, one participant expresses difficulty in finding a solution that satisfies all unique digit constraints for the letters involved.
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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