Setting up a spreadsheet to generate all possible sums from single, double or triple on each dart, as well as 25 or 50 for outer and inner bullseyes, I was able to produce all numbers through 100, but no score of 101, making that the smallest value that cannot be obtained with two darts. 103, 104, 106, 107, 109, 112, 113,115, 116, 118, 119 also cannot be obtained. 120 is the maximum score for two darts (both triple 20).
Quite right, I added the 25 and 50 at the end of the calculations, and missed that one! 103 is therefore the smallest number that cannot be scored with two darts.
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