Question 1198924
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The letters P, Q and R each stands for a different digit in the alphametric (PP)^2 + (PQ)^2 = QRQR. 
(Here, PP means a two-digit number, like 33.) If PP and PQ are consecutive numbers, then the value of P+Q + R is
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First notice that since the sum QRQR is a 4-digit number, the numbers PP and PQ can not be too large.

Indeed, P must be less than 7; otherwise the sum  (PP)^2 + (PQ)^2 will be 5-digit number.



Having it, there are not so many options for you to check: all possible oprtions are

(1)    PP = 66  PQ = 67

(2)    PP = 55  PQ = 56

(3)    PP = 44  PQ = 45

(4)    PP = 33  PQ = 34

(5)    PP = 22  PQ = 23

(6)    PP = 11  PQ = 12


It gives for  (PP)^2 + (PQ)^2  these possible values

(1)                8845

(2)                6161

(3)                3961

(4)                2245

(5)                1013

(6)                 265


Of these options, only (2) has the reqired form, with the number 6161.


So, P = 5, Q = 6, R = 1,

and P + Q + R = 5 + 6 + 1 = 12.    <U>ANSWER</U>
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Solved.