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there are 999 - 100 + 1 = 900 positive triple digit positive integers, between 100 and 999.(e.g. there are 102 - 100 + 1 = 3 triple digit integers between 100 and 102,namely 100, 101 and 102.)multiply that by 2 to take in consideration of the negative integers,you have 1800 triple digit integers.
999 EDIT Wrong. It has to have three digits, so it's in the range between 100 and 999. The lowest one is 100, but it's an even number, so the next one is 101, which is an odd one.
There is no set of three consecutive even integers whose sum is 999. There are two other sets; one is odd, the other is mixed. The odd set is 331, 333 and 335. The mixed set is 332, 333 and 334.
Of the 729 numbers that satisfy the requirement of positive integers, 104 are divisible by 7.
Suppose the sum is SS = 100 + 101 + ... + 998 + 999 Also, writing it in reverse order gives S = 999 + 998 + ... + 101 + 100 so, adding the two together, 2S = 1099 + 1099 + ... + 1099 + 1099 where there are 900 such terms. So S = 1099*900/2 = 494550.