In two or more consecutive set of integers, how many sets of integers are there when all integers are added in the set, the sum total becomes 2009?
Answer
5 sets
Solution
According to 2009 = 1 × 209 = 7 × 287 = 41 × 49, the sum total number of consecutive set of integers whose central number is 287, 49, and 41 becomes 2009.
In addition, according to 2009/2=1004.5, the sum total of 1004 and 1005 becomes 2009.
Furthermore, according to 2009 = 7 × 287 = 7 × 2 × 143.5, the sum total of 14 consecutive set of integers whose center is 143 and 144 becomes 2009.
Thus there are five sets altogether.
Answer
5 sets
Solution
According to 2009 = 1 × 209 = 7 × 287 = 41 × 49, the sum total number of consecutive set of integers whose central number is 287, 49, and 41 becomes 2009.
In addition, according to 2009/2=1004.5, the sum total of 1004 and 1005 becomes 2009.
Furthermore, according to 2009 = 7 × 287 = 7 × 2 × 143.5, the sum total of 14 consecutive set of integers whose center is 143 and 144 becomes 2009.
Thus there are five sets altogether.
