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The highest 3-digit number is 999. It's the 999th counting number.

The first 99 counting numbers have fewer than 3 digits.

So there are (999 - 99) = 900 positive 3-digit numbers.
The first is 100, the last is 999.

100 + 999 = 1,099
101 + 998 = 1,099
102 + 997 = 1,099
.
.
.
There are (900/2) = 450 pairs; each pair adds up to 1,099.

The sum of all pairs is (450 x 1,099) = 494,550 .

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15y ago

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