document.write( "Question 1186692: How many different integers can be represented as a sum of four distinct numbers chosen from the set (5,9,13,17,…,49) \n" ); document.write( "

Algebra.Com's Answer #817645 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "How many different integers can be represented as a sum of four distinct numbers chosen from the set (5,9,13,17,…,49)
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document.write( "The given set represents the terms of the arithmetic progression with the first term of 5 and the common difference of 4:\r\n" );
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document.write( "     = 5 + 4m,  m = 0, 1, 2, 3, . . . , 11.\r\n" );
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document.write( "In all, the set has 12 elements.\r\n" );
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document.write( "The sum of any 4 numbers of the set is the number of the form   ,\r\n" );
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document.write( "where  , ,   and    are different integer numbers between 0 and 11, inclusive.\r\n" );
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document.write( "The minimum value of such sum    is, OBVIOUSLY,  0+1+2+3 = 6.\r\n" );
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document.write( "The maximum value of such sum    is, OBVIOUSLY,  8+9+10+11 = 38.\r\n" );
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document.write( "It is clear that any index from 6 to 38 can be obtained as the sum of this form  .\r\n" );
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document.write( "THEREFORE, the  ANSWER to the problem's question is  38 - 6 + 1 = 33.\r\n" );
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