Maths Olympiad Prep

Library /IMO Shortlist

IMO Shortlist

365 problems here, rated 6.8 to 9.2 on our scale (National Olympiad to IMO level). 236 of them ask for a proof. Years covered: 2006–2021.

Algebra 122Combinatorics 89Geometry 86Number theory 68
#TopicDiffTypeYear
1 Number theory 6.8 proof — open
2 Algebra 6.8 answer — open
3 Algebra 7.2 answer — open
4 Combinatorics 7.3 answer — open
5 Combinatorics 7.4 answer — open
6 Number theory 7.5 answer — open
7 Algebra 7.5 answer — open
8 Combinatorics 7.5 answer — open
9 Number theory 7.5 answer — open
10 Algebra 7.5 proof 2020 open
11 Algebra 7.5 answer — open
12 Algebra 7.5 answer — open
13 Algebra 7.5 proof 2006 open
14 Number theory 7.6 proof 2007 open
15 Number theory 7.6 answer — open
16 Combinatorics 7.6 answer — open
17 Algebra 7.6 proof — open
18 Algebra 7.6 proof — open
19 Number theory 7.6 answer — open
20 Algebra 7.6 answer — open
21 Algebra 7.6 proof 2021 open
22 Algebra 7.6 proof — open
23 Combinatorics 7.6 answer — open
24 Number theory 7.7 answer — open
25 Algebra 7.7 answer — open
26 Geometry 7.7 answer — open
27 Number theory 7.7 answer — open
28 Algebra 7.7 proof 2006 open
29 Algebra 7.7 answer — open
30 Combinatorics 7.7 proof — open
31 Combinatorics 7.7 answer — open
32 Number theory 7.7 proof 2007 open
33 Combinatorics 7.7 answer — open
34 Number theory 7.8 answer — open
35 Combinatorics 7.8 proof — open
36 Geometry 7.8 answer — open
37 Algebra 7.8 answer — open
38 Algebra 7.8 answer — open
39 Number theory 7.8 proof 2021 open
40 Algebra 7.8 answer — open
41 Algebra 7.8 answer — open
42 Number theory 7.9 proof 2006 open
43 Combinatorics 7.9 proof 2019 open
44 Geometry 7.9 answer — open
45 Algebra 7.9 answer — open
46 Algebra 7.9 answer — open
47 Algebra 7.9 answer — open
48 Number theory 7.9 proof 2019 open
49 Number theory 7.9 proof 2006 open
50 Algebra 7.9 answer — open
51 Number theory 7.9 answer — open
52 Algebra 7.9 answer — open
53 Combinatorics 7.9 answer — open
54 Combinatorics 8.0 proof 2007 open
55 Algebra 8.0 proof — open
56 Number theory 8.0 proof — open
57 Algebra 8.0 answer — open
58 Algebra 8.0 answer — open
59 Algebra 8.0 answer — open
60 Algebra 8.0 proof 2019 open
61 Algebra 8.0 answer — open
62 Algebra 8.0 answer — open
63 Combinatorics 8.0 proof — open
64 Algebra 8.0 proof 2007 open
65 Number theory 8.0 proof 2019 open
66 Number theory 8.0 answer — open
67 Number theory 8.0 proof 2019 open
68 Algebra 8.0 answer — open
69 Algebra 8.0 answer — open
70 Algebra 8.1 proof 2020 open
71 Geometry 8.1 answer — open
72 Algebra 8.1 answer — open
73 Geometry 8.1 answer — open
74 Geometry 8.1 answer — open
75 Algebra 8.1 proof — open
76 Algebra 8.1 answer — open
77 Algebra 8.1 answer — open
78 Number theory 8.1 proof 2007 open
79 Algebra 8.1 answer — open
80 Geometry 8.1 answer — open
81 Number theory 8.1 answer — open
82 Number theory 8.1 answer — open
83 Algebra 8.1 proof 2011 open
84 Combinatorics 8.1 proof 2020 open
85 Number theory 8.1 proof 2007 open
86 Geometry 8.1 proof 2007 open
87 Number theory 8.2 proof — open
88 Number theory 8.2 answer — open
89 Number theory 8.2 answer — open
90 Algebra 8.2 answer — open
91 Number theory 8.2 answer — open
92 Number theory 8.2 answer — open
93 Combinatorics 8.2 answer — open
94 Geometry 8.2 proof — open
95 Geometry 8.2 proof — open
96 Geometry 8.2 proof — open
97 Algebra 8.2 answer — open
98 Number theory 8.2 proof — open
99 Algebra 8.2 answer — open
100 Algebra 8.2 answer — open
101 Number theory 8.2 answer — open
102 Geometry 8.2 answer — open
103 Algebra 8.2 answer — open
104 Geometry 8.2 proof — open
105 Geometry 8.2 proof 2007 open
106 Algebra 8.2 answer — open
107 Combinatorics 8.2 proof — open
108 Combinatorics 8.2 answer — open
109 Combinatorics 8.3 proof 2021 open
110 Geometry 8.3 proof — open
111 Combinatorics 8.3 proof — open
112 Number theory 8.3 answer — open
113 Geometry 8.3 proof 2006 open
114 Algebra 8.3 proof 2007 open
115 Combinatorics 8.3 answer — open
116 Geometry 8.3 proof 2011 open
117 Combinatorics 8.3 answer — open
118 Geometry 8.3 proof — open
119 Geometry 8.3 proof — open
120 Geometry 8.3 proof — open
121 Number theory 8.3 answer — open
122 Algebra 8.3 answer — open
123 Algebra 8.3 answer — open
124 Geometry 8.3 proof — open
125 Geometry 8.3 proof 2006 open
126 Algebra 8.3 answer — open
127 Geometry 8.4 proof 2007 open
128 Combinatorics 8.4 answer — open
129 Geometry 8.4 proof 2019 open
130 Algebra 8.4 answer — open
131 Algebra 8.4 proof 2019 open
132 Number theory 8.4 proof — open
133 Algebra 8.4 answer — open
134 Combinatorics 8.4 proof 2019 open
135 Geometry 8.4 proof — open
136 Combinatorics 8.4 answer — open
137 Geometry 8.4 proof — open
138 Algebra 8.4 answer — open
139 Algebra 8.4 proof — open
140 Geometry 8.4 proof — open
141 Geometry 8.4 proof 2011 open
142 Number theory 8.4 answer — open
143 Geometry 8.4 proof 2007 open
144 Algebra 8.4 answer — open
145 Combinatorics 8.4 answer — open
146 Algebra 8.4 proof 2007 open
147 Algebra 8.4 proof — open
148 Algebra 8.4 answer — open
149 Algebra 8.5 answer — open
150 Geometry 8.5 proof 2016 open
151 Algebra 8.5 proof 2006 open
152 Combinatorics 8.5 proof — open
153 Algebra 8.5 answer — open
154 Geometry 8.5 answer — open
155 Geometry 8.5 proof — open
156 Number theory 8.5 answer — open
157 Combinatorics 8.5 proof 2007 open
158 Algebra 8.5 proof 2021 open
159 Combinatorics 8.5 answer — open
160 Algebra 8.5 proof 2019 open
161 Combinatorics 8.5 proof 2006 open
162 Combinatorics 8.5 proof 2019 open
163 Algebra 8.5 answer — open
164 Geometry 8.5 proof — open
165 Geometry 8.5 proof 2019 open
166 Algebra 8.5 proof — open
167 Number theory 8.5 proof — open
168 Geometry 8.5 proof 2011 open
169 Algebra 8.5 answer — open
170 Algebra 8.5 answer — open
171 Combinatorics 8.5 answer — open
172 Algebra 8.5 answer — open
173 Geometry 8.5 answer — open
174 Algebra 8.6 proof — open
175 Algebra 8.6 proof 2011 open
176 Algebra 8.6 proof 2019 open
177 Combinatorics 8.6 answer — open
178 Geometry 8.6 proof — open
179 Geometry 8.6 proof 2019 open
180 Combinatorics 8.6 answer — open
181 Algebra 8.6 answer — open
182 Number theory 8.6 proof — open
183 Algebra 8.6 answer — open
184 Number theory 8.6 answer — open
185 Algebra 8.6 proof — open
186 Algebra 8.6 proof 2016 open
187 Algebra 8.6 proof — open
188 Algebra 8.6 proof — open
189 Combinatorics 8.6 answer — open
190 Combinatorics 8.6 proof 2020 open
191 Geometry 8.6 proof — open
192 Algebra 8.6 proof — open
193 Combinatorics 8.6 proof — open
194 Geometry 8.6 proof — open
195 Combinatorics 8.7 proof — open
196 Algebra 8.7 proof 2019 open
197 Geometry 8.7 proof — open
198 Number theory 8.7 proof 2016 open
199 Number theory 8.7 proof — open
200 Number theory 8.7 proof 2021 open
201 Number theory 8.7 proof 2016 open
202 Algebra 8.7 proof 2020 open
203 Geometry 8.7 proof — open
204 Number theory 8.7 proof 2019 open
205 Algebra 8.7 answer — open
206 Algebra 8.7 proof — open
207 Geometry 8.7 answer — open
208 Algebra 8.7 answer — open
209 Geometry 8.7 proof 2006 open
210 Geometry 8.7 proof — open
211 Number theory 8.7 proof — open
212 Algebra 8.7 proof 2020 open
213 Geometry 8.7 proof — open
214 Combinatorics 8.7 answer — open
215 Algebra 8.7 answer — open
216 Geometry 8.7 proof 2016 open
217 Number theory 8.7 proof 2011 open
218 Geometry 8.7 proof — open
219 Number theory 8.7 proof 2007 open
220 Combinatorics 8.7 proof 2007 open
221 Geometry 8.7 proof — open
222 Geometry 8.7 proof — open
223 Number theory 8.7 proof — open
224 Geometry 8.7 proof 2007 open
225 Algebra 8.7 answer — open
226 Geometry 8.7 proof — open
227 Combinatorics 8.7 proof — open
228 Number theory 8.7 answer — open
229 Algebra 8.7 proof 2019 open
230 Geometry 8.7 proof 2006 open
231 Algebra 8.7 answer — open
232 Algebra 8.7 answer — open
233 Algebra 8.7 proof 2006 open
234 Combinatorics 8.7 proof 2006 open
235 Algebra 8.7 proof 2006 open
236 Algebra 8.7 answer — open
237 Geometry 8.8 proof — open
238 Algebra 8.8 proof — open
239 Algebra 8.8 proof — open
240 Geometry 8.8 proof — open
241 Combinatorics 8.8 answer — open
242 Combinatorics 8.8 proof — open
243 Geometry 8.8 proof 2006 open
244 Geometry 8.8 proof — open
245 Number theory 8.8 proof — open
246 Combinatorics 8.8 proof — open
247 Geometry 8.8 proof 2016 open
248 Combinatorics 8.8 answer — open
249 Combinatorics 8.8 answer — open
250 Algebra 8.8 proof 2021 open
251 Geometry 8.8 proof 2006 open
252 Combinatorics 8.8 proof — open
253 Geometry 8.8 answer — open
254 Algebra 8.8 answer — open
255 Algebra 8.8 proof 2011 open
256 Algebra 8.8 proof — open
257 Algebra 8.8 proof — open
258 Number theory 8.8 proof 2019 open
259 Geometry 8.8 proof 2011 open
260 Geometry 8.8 proof 2016 open
261 Geometry 8.8 proof — open
262 Combinatorics 8.8 proof 2020 open
263 Combinatorics 8.8 proof 2021 open
264 Algebra 8.8 answer — open
265 Number theory 8.8 proof 2019 open
266 Combinatorics 8.8 proof — open
267 Geometry 8.8 proof 2006 open
268 Number theory 8.8 answer — open
269 Number theory 8.8 answer — open
270 Geometry 8.8 proof 2007 open
271 Geometry 8.8 proof 2021 open
272 Combinatorics 8.8 proof 2016 open
273 Geometry 8.8 proof — open
274 Combinatorics 8.8 proof — open
275 Combinatorics 8.8 proof — open
276 Algebra 8.8 proof — open
277 Geometry 8.8 proof — open
278 Combinatorics 8.8 proof — open
279 Geometry 8.9 proof 2016 open
280 Number theory 8.9 proof 2021 open
281 Combinatorics 8.9 answer — open
282 Combinatorics 8.9 proof — open
283 Number theory 8.9 proof — open
284 Geometry 8.9 answer — open
285 Geometry 8.9 proof — open
286 Combinatorics 8.9 proof — open
287 Geometry 8.9 proof 2016 open
288 Geometry 8.9 proof 2019 open
289 Combinatorics 8.9 answer — open
290 Number theory 8.9 proof 2007 open
291 Combinatorics 8.9 proof — open
292 Algebra 8.9 proof 2019 open
293 Combinatorics 8.9 proof — open
294 Algebra 8.9 proof 2006 open
295 Combinatorics 8.9 answer — open
296 Combinatorics 8.9 proof — open
297 Number theory 8.9 proof 2016 open
298 Geometry 8.9 proof — open
299 Number theory 8.9 proof — open
300 Number theory 8.9 proof — open
301 Algebra 8.9 answer — open
302 Combinatorics 8.9 answer — open
303 Algebra 8.9 proof 2007 open
304 Geometry 8.9 proof 2006 open
305 Number theory 8.9 proof — open
306 Geometry 9.0 proof 2019 open
307 Geometry 9.0 proof — open
308 Number theory 9.0 proof — open
309 Number theory 9.0 proof — open
310 Number theory 9.0 proof — open
311 Combinatorics 9.0 proof 2021 open
312 Algebra 9.0 proof — open
313 Number theory 9.0 proof — open
314 Geometry 9.0 proof 2006 open
315 Number theory 9.0 proof 2011 open
316 Combinatorics 9.0 proof 2019 open
317 Algebra 9.0 proof — open
318 Geometry 9.0 proof 2019 open
319 Number theory 9.0 proof — open
320 Algebra 9.0 proof — open
321 Number theory 9.0 proof — open
322 Algebra 9.0 proof — open
323 Geometry 9.0 proof — open
324 Combinatorics 9.0 proof — open
325 Geometry 9.0 proof — open
326 Combinatorics 9.0 proof — open
327 Combinatorics 9.0 proof — open
328 Algebra 9.0 proof — open
329 Geometry 9.0 proof 2021 open
330 Algebra 9.0 proof — open
331 Number theory 9.0 proof — open
332 Algebra 9.0 proof — open
333 Combinatorics 9.0 proof — open
334 Algebra 9.0 proof — open
335 Algebra 9.0 proof 2020 open
336 Algebra 9.0 proof 2021 open
337 Geometry 9.0 proof 2021 open
338 Algebra 9.1 proof 2016 open
339 Algebra 9.1 answer — open
340 Combinatorics 9.1 proof 2011 open
341 Geometry 9.1 proof 2006 open
342 Combinatorics 9.1 proof — open
343 Algebra 9.1 proof — open
344 Combinatorics 9.1 proof 2006 open
345 Algebra 9.1 proof — open
346 Combinatorics 9.1 proof 2007 open
347 Combinatorics 9.1 proof 2007 open
348 Geometry 9.1 proof 2019 open
349 Combinatorics 9.1 answer — open
350 Combinatorics 9.1 answer — open
351 Geometry 9.1 proof — open
352 Combinatorics 9.1 answer — open
353 Combinatorics 9.1 proof — open
354 Algebra 9.1 proof — open
355 Combinatorics 9.1 proof 2019 open
356 Combinatorics 9.2 proof 2020 open
357 Combinatorics 9.2 proof 2019 open
358 Combinatorics 9.2 proof — open
359 Combinatorics 9.2 proof — open
360 Combinatorics 9.2 proof 2021 open
361 Combinatorics 9.2 proof 2006 open
362 Combinatorics 9.2 proof 2016 open
363 Combinatorics 9.2 proof 2016 open
364 Combinatorics 9.2 proof — open
365 Combinatorics 9.2 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.