document.write( "Question 1210229: Find the number of subsets of
\n" ); document.write( "S = \{1, 3, 8, 17, 30, 36, 47, 58\},
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Algebra.Com's Answer #851696 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Find the number of subsets of
\n" ); document.write( "S = {1, 3, 8, 17, 30, 36, 47, 58},
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\n" ); document.write( "(Note that for the empty subset, we take the sum of the elements as 0.)
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document.write( "Looking into the given set, we see that all numbers 30, 36, 47, 58 can be excluded \r\n" );
document.write( "from consideration, since each of them is just greater than 20.\r\n" );
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document.write( "So, the original set of 8 numbers can be reduced to the set of 4 numbers {1, 3, 8, 17}.\r\n" );
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document.write( "For this set of 4 numbers, the number of all its subsets is   = 16.\r\n" );
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document.write( "But not all of these 16 subsets fit the condition.\r\n" );
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document.write( "We should exclude the subsets that produce the sum 20 or greater.\r\n" );
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document.write( "So, the subsets to exclude are  these 6 subsets \r\n" );
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document.write( "    {1, 3, 8, 17}, {1, 3, 17}, {1, 8, 17}, {3, 8, 17}, {3,17}, {8,17}.\r\n" );
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document.write( "The rest of the subsets, 16 - 6 = 10, fit the condition.\r\n" );
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document.write( "ANSWER.  There are 10 subsets that fit the condition.\r\n" );
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