There are 2 ways we can attack this problem...
Method 1:
Notice that the subtraction result for every 2 pairs has the answer of 2.
Since there are 50 pairs that have the result of 2 this is 50(2) or 100.
Method 2:
We can use Gaussean Addition...
The normally the formula we would use is n(n+1)/2 but we are adding all the added pairs, all the subtracted pairs and then subtracting them (if that made any sense...). Since 99+3 = 102 we multiply that by 50/2 or 25. 102 x 25 = 2550.
Each pair from the subtracting side sums up to 98. We multiply 98 x 25 to get 2450. 2550 - 2450 = 100.
100 is my final answer...
