document.write( "Question 1027853: Five different positive integers added two at a time give the
\n" ); document.write( "following sums: 16, 20, 22, 23, 25, 28, 29, 30, 34, and 37. Find
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Algebra.Com's Answer #643115 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We let the numbers be a < b < c < d < e\r\n" );
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document.write( "Then the smallest two, a and b, must have sum 16,\r\n" );
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document.write( "a + b = 16\r\n" );
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document.write( "and the largest two, d and e, must have sum 37,\r\n" );
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document.write( "d + e = 37.\r\n" );
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document.write( "[Those are the only two pairs that we can be sure\r\n" );
document.write( "have the smallest and largest sums.  We can't be\r\n" );
document.write( "sure about the other pairs.]\r\n" );
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document.write( "If the smallest number, a, is too small we won't\r\n" );
document.write( "be able to get all those large sums.  So let's\r\n" );
document.write( "take the smallest, a, to be as large as possible \r\n" );
document.write( "We'll begin by trying a=7 and b=9, so that 7+9=16.\r\n" );
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document.write( "We need to be able to get 20 by adding two numbers, \r\n" );
document.write( "so we need to add 13 to the 7 to get the 20. [Note\r\n" );
document.write( "that we'd have to add 4 to the 9, and 4 is too small.] \r\n" );
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document.write( "We take c=13, so that 7+13=20.\r\n" );
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document.write( "We can now also get 22, since 9+13=22.\r\n" );
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document.write( "We have so far, a=7, b=9, c=13. \r\n" );
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document.write( "So d is larger than 13.\r\n" );
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document.write( "d can't be 14 because 14+13=27 which is not one of \r\n" );
document.write( "the sums.\r\n" );
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document.write( "d can't be 15 because 15+9=24 which is not one of \r\n" );
document.write( "the sums.\r\n" );
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document.write( "But d can be 16, because 7+16=23, which is one of \r\n" );
document.write( "the sums.\r\n" );
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document.write( "Also 9+16=25, which is one of the sums.\r\n" );
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document.write( "We have so far, a=7, b=9, c=13, d=16\r\n" );
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document.write( "Now since d + e = 37, e can only be 21, \r\n" );
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document.write( "so that 16+21=37\r\n" );
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document.write( "Answer: a=7, b=9, c=13, d=16, e=21\r\n" );
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document.write( "Checking:\r\n" );
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document.write( " 7+ 9 = 16\r\n" );
document.write( " 7+13 = 20\r\n" );
document.write( " 9+13 = 22\r\n" );
document.write( " 7+16 = 23\r\n" );
document.write( " 9+16 = 25\r\n" );
document.write( " 7+21 = 28\r\n" );
document.write( "13+16 = 29\r\n" );
document.write( " 9+21 = 30\r\n" );
document.write( "13+21 = 34\r\n" );
document.write( "16+21 = 37\r\n" );
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document.write( "The product is 7*9*13*16*21 = 275184\r\n" );
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document.write( "Edwin

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