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 #832596 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Hint:\r
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\n" ); document.write( "\n" ); document.write( "1^2 = 1
\n" ); document.write( "2^2 = 4
\n" ); document.write( "3^2 = 9
\n" ); document.write( "4^2 = 16
\n" ); document.write( "5^2 = 25
\n" ); document.write( "6^2 = 36
\n" ); document.write( "7^2 = 49
\n" ); document.write( "8^2 = 64
\n" ); document.write( "9^2 = 81
\n" ); document.write( "Focus on the units digit of each result to get this sequence: 1, 4, 9, 6, 5, 6, 9, 4, 1
\n" ); document.write( "Notice we have symmetry.\r
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\n" ); document.write( "\n" ); document.write( "Sort the values and toss out any duplicates to get: 1, 4, 5, 6, 9\r
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\n" ); document.write( "\n" ); document.write( "Another hint:\r
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\n" ); document.write( "\n" ); document.write( "Q = P+1 since PP and PQ are consecutive numbers (eg: 64 and 65)
\n" ); document.write( "PP and PQ are of different parity (one is odd, the other even, in either order)
\n" ); document.write( "(PP)^2 and (PQ)^2 are of different parity. I'll leave the proof for the reader.\r
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\n" ); document.write( "\n" ); document.write( "odd + even = odd
\n" ); document.write( "which means QRQR is odd, and R itself is odd
\n" ); document.write( "The possible values of R is from the set {1,3,5,7,9}
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