The "one number is missing" method obviously won't work (2 + 4 = 1 + 5) but I'd still employ it...
Missing: 70, 13
5050 - 4967 = 83 -> missing numbers < 83
Finde one missing number: 82, 81, 80, ... 70
83 - 70 = 13
Missing numbers: 70, 13
Can't come up with an elegant algorithm. Do you know one?
Well, there is an "elegant" algorithm. (I put elegant in quotes because only mathematicians would think it so. The rest of us would just go through the numbers one by one and do it more quickly.)
Calculate 100 factorial. Then calculate the product of all 98 numbers on the list. The quotient is the product of the two missing numbers.
Now you have a system of two equations in two variables and you can easily solve for the missing numbers.
D'oh.
Thanks, Guy.