document.write( "Question 1198924: 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 \n" ); document.write( "

Algebra.Com's Answer #832607 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The letters P, Q and R each stands for a different digit in the alphametric (PP)^2 + (PQ)^2 = QRQR.
\n" ); document.write( "(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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document.write( "First notice that since the sum QRQR is a 4-digit number, the numbers PP and PQ can not be too large.\r\n" );
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document.write( "Indeed, P must be less than 7; otherwise the sum  (PP)^2 + (PQ)^2 will be 5-digit number.\r\n" );
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document.write( "Having it, there are not so many options for you to check: all possible oprtions are\r\n" );
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document.write( "(1)    PP = 66  PQ = 67\r\n" );
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document.write( "(2)    PP = 55  PQ = 56\r\n" );
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document.write( "(3)    PP = 44  PQ = 45\r\n" );
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document.write( "(4)    PP = 33  PQ = 34\r\n" );
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document.write( "(5)    PP = 22  PQ = 23\r\n" );
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document.write( "(6)    PP = 11  PQ = 12\r\n" );
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document.write( "It gives for  (PP)^2 + (PQ)^2  these possible values\r\n" );
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document.write( "(1)                8845\r\n" );
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document.write( "(2)                6161\r\n" );
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document.write( "(3)                3961\r\n" );
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document.write( "(4)                2245\r\n" );
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document.write( "(5)                1013\r\n" );
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document.write( "(6)                 265\r\n" );
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document.write( "Of these options, only (2) has the reqired form, with the number 6161.\r\n" );
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document.write( "So, P = 5, Q = 6, R = 1,\r\n" );
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document.write( "and P + Q + R = 5 + 6 + 1 = 12.    ANSWER\r\n" );
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