Algebra.Com's Answer #847241 by ikleyn(52794)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "How many different integers can be represented as a sum of four distinct numbers chosen from the set {5,12,19,26,..., 110} ?
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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 7:\r\n" );
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document.write( "  = 5 + 7m, m = 0, 1, 2, 3, . . . , 15.\r\n" );
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document.write( "In all, the set has 16 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 16, 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, 12+13+14+15 = 54.\r\n" );
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document.write( "It is clear that any index from 6 to 54 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 54 - 5 = 49.\r\n" );
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document.write( "ANSWER. 49 different integers can be represented as the sum.\r\n" );
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document.write( "Solved.\r
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