document.write( "Question 547110: How many positive two-digit numbers have the square of an integer as the product of their digits? \n" ); document.write( "
Algebra.Com's Answer #356241 by Edwin McCravy(20054)\"\" \"About 
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document.write( "All the squares of natural numbers possible by taking the product of the\r\n" );
document.write( "digits of a two-digit number are these: \r\n" );
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document.write( "0,1,4,9,16,25,36,49,64,81 \r\n" );
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document.write( "since the largest two digit number is 99, which has product of digits 81.  \r\n" );
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document.write( "The numbers 10,20,30,..,90  account for 9 two-digit number which have 0 as\r\n" );
document.write( "their product of digits.  That's 9.\r\n" );
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document.write( "11 is the only one that has product of digits 1. That makes 10.\r\n" );
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document.write( "14, 22, and 41 are the only ones with product of digits 4.  That makes 13.\r\n" );
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document.write( "19, 33, and 91 are the only ones with product of digits 9.  That makes 16.\r\n" );
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document.write( "28, 44, and 82 are the only ones with product of digits 16.  That makes 19.\r\n" );
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document.write( "55 is the only one with product of digits 25.  That makes 20.\r\n" );
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document.write( "49, 66, and 94 are the only ones with product of digits 36.  That makes 23.\r\n" );
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document.write( "77 is the only one with product of digits 49.  That makes 24.\r\n" );
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document.write( "88 is the olny one with product of digits 64.  That makes 25.\r\n" );
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document.write( "99 is the only one with product of digits 81.  That makes 26.\r\n" );
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document.write( "Answer: 26.\r\n" );
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document.write( "Edwin
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