- #1

K Sengupta

- 113

- 0

(PQR)

^{2}+ (STUQ)

^{2}= (SVWX)

^{2}

__Note__: None of P and S can be zero.

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In summary, a cryptarithmetic equation is given where letters P, Q, R, S, T, U, V, W, X represent decimal digits from 0 to 9. The equation is (PQR)2 + (STUQ)2 = (SVWX)2, where none of P and S can be zero. After discussing various solutions and errors, it is determined that a solution for all unique PQRSTUVWX cannot be found.

- #1

K Sengupta

- 113

- 0

(PQR)

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- #2

dsa

- 11

- 0

(125)^{2} + (7812)^{2} = (7813)^{2}

- #3

K Sengupta

- 113

- 0

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.

- #4

dsa

- 11

- 0

OK, this one is better

(480)^{2} + (1768)^{2} = (1832)^{2}

- #5

K Sengupta

- 113

- 0

dsa said:OK, this one is better

(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.

- #6

dsa

- 11

- 0

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

Cryptarithmetic is a type of mathematical puzzle in which numbers are represented by letters and the goal is to decipher the correct numerical values for each letter in order to solve the equation.

The "Sum the squares cryptarithmetically, get square" puzzle is a specific type of cryptarithmetic problem where the equation involves squaring numbers and finding the sum of the squared values. The end result should also be a perfect square number.

The first step in solving this puzzle is to identify the numerical constraints, such as the number of digits in each number and any specific digits that are known. Then, it is helpful to start with the largest possible numbers for each letter and work backwards to find the correct values. It may also be helpful to use a process of elimination to rule out certain values that do not fit the constraints.

Some strategies that can be helpful in solving this type of puzzle include looking for patterns or relationships between the numbers, breaking the equation into smaller parts to solve separately, and using trial and error to test different values for each letter until a solution is found.

For beginners, it can be helpful to start with simpler cryptarithmetic problems and work up to more complex ones like the "Sum the squares cryptarithmetically, get square" puzzle. It is also important to be patient and not give up too quickly, as solving these types of puzzles can take time and require multiple attempts before finding the correct solution.

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