Maths Olympiad Prep

Library /USAMO

USAMO

156 problems here, rated 6 to 8.2 on our scale (National Olympiad to Shortlist). 47 of them ask for a proof. Years covered: 2009–2010.

Algebra 56Combinatorics 44Geometry 34Number theory 22
#TopicDiffTypeYear
1 Algebra 6.0 answer — open
2 Geometry 6.0 answer — open
3 Geometry 6.0 answer — open
4 Geometry 6.1 answer — open
5 Algebra 6.1 answer — open
6 Algebra 6.2 answer — open
7 Number theory 6.3 proof — open
8 Number theory 6.3 answer — open
9 Number theory 6.3 answer — open
10 Algebra 6.4 answer — open
11 Algebra 6.5 answer — open
12 Algebra 6.5 answer — open
13 Algebra 6.6 answer — open
14 Number theory 6.6 answer — open
15 Algebra 6.7 answer — open
16 Algebra 6.7 answer — open
17 Algebra 6.7 answer — open
18 Geometry 6.7 answer — open
19 Geometry 6.8 answer — open
20 Combinatorics 6.8 answer — open
21 Algebra 6.8 answer — open
22 Geometry 6.8 answer — open
23 Combinatorics 6.8 answer — open
24 Combinatorics 6.8 answer — open
25 Combinatorics 6.9 answer — open
26 Combinatorics 6.9 answer — open
27 Algebra 7.0 answer — open
28 Geometry 7.0 answer — open
29 Algebra 7.0 answer — open
30 Number theory 7.0 answer — open
31 Geometry 7.0 proof 2009 open
32 Geometry 7.0 proof — open
33 Combinatorics 7.0 answer — open
34 Geometry 7.0 answer — open
35 Combinatorics 7.0 answer — open
36 Combinatorics 7.0 proof — open
37 Geometry 7.0 answer — open
38 Algebra 7.1 answer — open
39 Number theory 7.1 answer — open
40 Algebra 7.1 answer — open
41 Number theory 7.1 proof — open
42 Number theory 7.1 answer — open
43 Algebra 7.1 answer — open
44 Geometry 7.1 answer — open
45 Combinatorics 7.1 proof — open
46 Algebra 7.1 answer — open
47 Algebra 7.1 answer — open
48 Combinatorics 7.1 answer — open
49 Number theory 7.2 answer — open
50 Algebra 7.2 proof 2009 open
51 Combinatorics 7.2 proof — open
52 Algebra 7.2 answer — open
53 Combinatorics 7.2 answer — open
54 Algebra 7.2 proof 2010 open
55 Geometry 7.2 answer — open
56 Combinatorics 7.2 answer — open
57 Number theory 7.2 answer — open
58 Combinatorics 7.2 answer — open
59 Combinatorics 7.3 answer — open
60 Combinatorics 7.3 proof — open
61 Combinatorics 7.3 proof — open
62 Algebra 7.3 answer — open
63 Algebra 7.3 answer — open
64 Algebra 7.3 proof — open
65 Algebra 7.3 answer — open
66 Algebra 7.3 answer — open
67 Combinatorics 7.3 answer — open
68 Algebra 7.3 answer — open
69 Geometry 7.3 proof — open
70 Geometry 7.3 proof — open
71 Combinatorics 7.4 proof 2009 open
72 Algebra 7.4 answer — open
73 Geometry 7.4 proof 2010 open
74 Algebra 7.4 proof — open
75 Algebra 7.4 answer — open
76 Algebra 7.4 answer — open
77 Algebra 7.4 answer — open
78 Algebra 7.4 proof — open
79 Geometry 7.4 proof — open
80 Geometry 7.4 answer — open
81 Geometry 7.4 proof — open
82 Combinatorics 7.4 answer — open
83 Combinatorics 7.4 proof — open
84 Algebra 7.4 answer — open
85 Combinatorics 7.4 answer — open
86 Combinatorics 7.4 answer — open
87 Algebra 7.4 answer — open
88 Geometry 7.4 answer — open
89 Geometry 7.5 proof 2009 open
90 Algebra 7.5 answer — open
91 Algebra 7.5 answer — open
92 Number theory 7.5 answer — open
93 Geometry 7.5 answer — open
94 Algebra 7.5 proof 2010 open
95 Combinatorics 7.5 answer — open
96 Algebra 7.5 answer — open
97 Geometry 7.5 proof — open
98 Geometry 7.5 answer — open
99 Combinatorics 7.5 answer — open
100 Number theory 7.5 proof — open
101 Combinatorics 7.5 answer — open
102 Number theory 7.5 proof 2009 open
103 Combinatorics 7.5 answer — open
104 Algebra 7.5 answer — open
105 Algebra 7.5 answer — open
106 Algebra 7.5 answer — open
107 Geometry 7.6 proof — open
108 Algebra 7.6 answer — open
109 Algebra 7.6 answer — open
110 Geometry 7.6 answer — open
111 Combinatorics 7.6 proof 2010 open
112 Number theory 7.6 answer — open
113 Geometry 7.6 answer — open
114 Number theory 7.6 answer — open
115 Geometry 7.6 proof 2010 open
116 Combinatorics 7.6 proof — open
117 Number theory 7.6 answer — open
118 Number theory 7.6 answer — open
119 Algebra 7.6 answer — open
120 Number theory 7.6 answer — open
121 Algebra 7.7 answer — open
122 Algebra 7.7 answer — open
123 Number theory 7.7 proof — open
124 Geometry 7.7 proof — open
125 Algebra 7.7 answer — open
126 Combinatorics 7.7 answer — open
127 Combinatorics 7.7 answer — open
128 Geometry 7.7 proof — open
129 Geometry 7.7 proof — open
130 Algebra 7.7 answer — open
131 Number theory 7.7 proof — open
132 Combinatorics 7.7 answer — open
133 Algebra 7.7 answer — open
134 Algebra 7.7 answer — open
135 Algebra 7.8 answer — open
136 Combinatorics 7.8 answer — open
137 Combinatorics 7.8 answer — open
138 Combinatorics 7.8 proof — open
139 Combinatorics 7.8 proof 2010 open
140 Geometry 7.8 answer — open
141 Algebra 7.8 answer — open
142 Combinatorics 7.9 proof — open
143 Combinatorics 7.9 proof — open
144 Combinatorics 7.9 answer — open
145 Algebra 7.9 answer — open
146 Algebra 8.0 answer — open
147 Geometry 8.0 proof — open
148 Number theory 8.0 proof — open
149 Combinatorics 8.0 proof — open
150 Algebra 8.0 answer — open
151 Combinatorics 8.0 proof — open
152 Number theory 8.0 proof — open
153 Geometry 8.0 proof — open
154 Combinatorics 8.0 answer — open
155 Combinatorics 8.1 proof — open
156 Combinatorics 8.2 proof — open
These are sorted by difficulty within the competition, but they aren't a course. The track is the route through, drawn from all the sources at once.