document.write( "Question 1197920: How many different integers can be represented as a sum of four distinct numbers chosen from the set {7,20,33,46,...,150}? \n" ); document.write( "
Algebra.Com's Answer #831381 by Edwin McCravy(20060)\"\" \"About 
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document.write( "That's the arithmetic sequence \r\n" );
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document.write( "7, 20, 33, 46, 59, 72, 85, 98, 111, 124, 137, 150\r\n" );
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document.write( "Make a new arithmetic sequence by subtracting 7 from every term:\r\n" );
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document.write( "0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143\r\n" );
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document.write( "Make another new arithmetic sequence by dividing every term by 13:\r\n" );
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document.write( "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\r\n" );
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document.write( "The smallest possible sum represented as a sum of four distinct \r\n" );
document.write( "numbers chosen from this sequence is 0+1+2+3 = 6\r\n" );
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document.write( "The largest possible sum represented by a sum of four distinct \r\n" );
document.write( "numbers chosen from it is 8+9+10+11 = 38\r\n" );
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document.write( "Every integer from 6 to 38 inclusive can be represented as a sum of four distinct numbers chosen from the set {0,1,2,3,...,11\r\n" );
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document.write( "That's 38-6+1 = 33 possible sums.  For every one of those sums, there is\r\n" );
document.write( "a corresponding sum of four distinct numbers chosen from the set {7,20,33,46,...,150}? \r\n" );
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document.write( "Answer: 33 different integers can be represented as a sum of four distinct numbers chosen from the set {7,20,33,46,...,150}\r\n" );
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document.write( "Edwin
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