Math puzzles!

8) 99

 Spoiler

2-41: 1/miss + 2x 1-20
42-60: 2-20 + 2x 20
61: 3x 7 + 2x 20
62: 2x 11 + 2x 20
63: 3x 13 + 2x 12
64: 2x 20 + 2x 12
65: 3x 13 + 2x 13
66: 3x 14 + 2x 12
67: 3x 19 + 2x 5
68: 3x 14 + 2x 13
69: 3x 15 + 2x 12
70: 3x 20 + 2x 5
71: 3x 15 + 2x 13
72: 3x 16 + 2x 12
73: 3x 19 + 2x 8
74: 3x 16 + 2x 13
75: 3x 15 + 2x 15
76: 3x 20 + 2x 8
77: 3x 17 + 2x 13
78: 3x 16 + 2x 15
79: 3x 19 + 2x 11
80: 3x 20 + 2x 10
81: 3x 17 + 2x 15
82: 3x 20 + 2x 11
83: 3x 19 + 2x 13
84: 3x 18 + 2x 15
85: 3x 15 + 2x 20
86: 3x 20 + 2x 13
87: 3x 19 + 2x 15
88: 3x 16 + 2x 20
89: 3x 19 + 2x 16
90: 3x 20 + 2x 15
91: 3x 17 + 2x 20
92: 3x 20 + 2x 16
93: 3x 19 + 2x 18
94: 3x 18 + 2x 20
95: 3x 19 + 2x 19
96: 3x 20 + 2x 18
97: 3x 19 + 2x 20
98: 3x 20 + 2x 19
99: Not possible! The highest number you can go with the second shot is 2x 20 = 40. So you need to get to 40 (or a lower even number) after the first shot. However, hitting 59 (or a higher odd number) with one shot isn't possible.
100: 3x 20 + 2x 20
101+: Not possible with only 2 darts.

Excellent, 99 is the correct answer

Now do it with three darts (At the very least you already know what's possible with 2 darts, so no need to check those