Maths Olympiad Prep

Library /IMO Shortlist

IMO Shortlist

367 problems here, rated 6.8 to 9.3 on our scale (National Olympiad to IMO level). 230 of them ask for a proof. Years covered: 2006–2021.

Algebra 123Combinatorics 84Geometry 86Number theory 74
#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 answer — open
36 Combinatorics 7.8 proof — open
37 Geometry 7.8 answer — open
38 Geometry 7.8 answer — open
39 Algebra 7.8 answer — open
40 Number theory 7.8 answer — open
41 Algebra 7.8 answer — open
42 Algebra 7.8 proof 2007 open
43 Number theory 7.8 proof 2021 open
44 Algebra 7.8 answer — open
45 Algebra 7.8 answer — open
46 Number theory 7.9 proof 2006 open
47 Combinatorics 7.9 proof 2019 open
48 Geometry 7.9 answer — open
49 Algebra 7.9 answer — open
50 Algebra 7.9 answer — open
51 Algebra 7.9 answer — open
52 Algebra 7.9 answer — open
53 Algebra 7.9 answer — open
54 Number theory 7.9 proof 2019 open
55 Number theory 7.9 proof 2006 open
56 Algebra 7.9 answer — open
57 Number theory 7.9 answer — open
58 Algebra 7.9 answer — open
59 Combinatorics 7.9 answer — open
60 Combinatorics 8.0 proof 2007 open
61 Algebra 8.0 proof — open
62 Number theory 8.0 proof — open
63 Algebra 8.0 answer — open
64 Algebra 8.0 answer — open
65 Algebra 8.0 answer — open
66 Algebra 8.0 proof 2019 open
67 Algebra 8.0 answer — open
68 Algebra 8.0 answer — open
69 Number theory 8.0 proof — open
70 Combinatorics 8.0 proof — open
71 Algebra 8.0 proof 2007 open
72 Number theory 8.0 proof 2019 open
73 Number theory 8.0 answer — open
74 Number theory 8.0 proof 2019 open
75 Algebra 8.0 answer — open
76 Algebra 8.0 answer — open
77 Algebra 8.1 proof 2020 open
78 Geometry 8.1 answer — open
79 Algebra 8.1 answer — open
80 Geometry 8.1 answer — open
81 Geometry 8.1 answer — open
82 Algebra 8.1 proof — open
83 Algebra 8.1 answer — open
84 Algebra 8.1 answer — open
85 Number theory 8.1 proof 2007 open
86 Algebra 8.1 answer — open
87 Geometry 8.1 answer — open
88 Number theory 8.1 answer — open
89 Number theory 8.1 answer — open
90 Algebra 8.1 proof 2011 open
91 Combinatorics 8.1 proof 2020 open
92 Number theory 8.1 proof 2007 open
93 Geometry 8.1 proof 2007 open
94 Number theory 8.2 proof — open
95 Number theory 8.2 answer — open
96 Geometry 8.2 proof — open
97 Number theory 8.2 answer — open
98 Algebra 8.2 answer — open
99 Number theory 8.2 answer — open
100 Number theory 8.2 answer — open
101 Combinatorics 8.2 answer — open
102 Geometry 8.2 proof — open
103 Geometry 8.2 proof — open
104 Geometry 8.2 proof — open
105 Algebra 8.2 answer — open
106 Number theory 8.2 proof — open
107 Algebra 8.2 answer — open
108 Algebra 8.2 answer — open
109 Number theory 8.2 answer — open
110 Geometry 8.2 answer — open
111 Algebra 8.2 answer — open
112 Geometry 8.2 proof — open
113 Geometry 8.2 proof 2007 open
114 Algebra 8.2 answer — open
115 Combinatorics 8.2 proof — open
116 Combinatorics 8.2 answer — open
117 Combinatorics 8.3 proof 2021 open
118 Geometry 8.3 proof — open
119 Combinatorics 8.3 proof — open
120 Number theory 8.3 answer — open
121 Geometry 8.3 proof 2006 open
122 Algebra 8.3 proof 2007 open
123 Combinatorics 8.3 answer — open
124 Geometry 8.3 proof 2011 open
125 Combinatorics 8.3 answer — open
126 Geometry 8.3 proof — open
127 Geometry 8.3 proof — open
128 Geometry 8.3 proof — open
129 Number theory 8.3 answer — open
130 Number theory 8.3 answer — open
131 Algebra 8.3 answer — open
132 Algebra 8.3 answer — open
133 Geometry 8.3 proof — open
134 Geometry 8.3 proof 2006 open
135 Algebra 8.3 answer — open
136 Geometry 8.4 proof 2007 open
137 Geometry 8.4 proof — open
138 Combinatorics 8.4 answer — open
139 Geometry 8.4 proof 2019 open
140 Algebra 8.4 answer — open
141 Algebra 8.4 proof 2019 open
142 Number theory 8.4 proof — open
143 Number theory 8.4 proof 2011 open
144 Algebra 8.4 answer — open
145 Combinatorics 8.4 proof 2019 open
146 Geometry 8.4 proof — open
147 Combinatorics 8.4 answer — open
148 Geometry 8.4 proof — open
149 Algebra 8.4 answer — open
150 Number theory 8.4 answer — open
151 Algebra 8.4 proof — open
152 Geometry 8.4 proof — open
153 Geometry 8.4 proof 2011 open
154 Number theory 8.4 answer — open
155 Geometry 8.4 proof 2007 open
156 Algebra 8.4 answer — open
157 Combinatorics 8.4 answer — open
158 Algebra 8.4 proof 2007 open
159 Algebra 8.4 proof — open
160 Algebra 8.4 answer — open
161 Algebra 8.5 answer — open
162 Geometry 8.5 proof 2016 open
163 Algebra 8.5 proof 2006 open
164 Combinatorics 8.5 proof — open
165 Combinatorics 8.5 answer — open
166 Algebra 8.5 answer — open
167 Geometry 8.5 answer — open
168 Geometry 8.5 proof — open
169 Number theory 8.5 answer — open
170 Combinatorics 8.5 proof 2007 open
171 Algebra 8.5 proof 2021 open
172 Combinatorics 8.5 answer — open
173 Algebra 8.5 proof 2019 open
174 Combinatorics 8.5 proof 2006 open
175 Combinatorics 8.5 proof 2019 open
176 Algebra 8.5 answer — open
177 Geometry 8.5 proof — open
178 Geometry 8.5 proof 2019 open
179 Algebra 8.5 proof — open
180 Number theory 8.5 proof — open
181 Geometry 8.5 proof 2011 open
182 Algebra 8.5 answer — open
183 Algebra 8.5 answer — open
184 Combinatorics 8.5 answer — open
185 Algebra 8.5 answer — open
186 Geometry 8.5 answer — open
187 Algebra 8.6 proof — open
188 Algebra 8.6 proof 2011 open
189 Algebra 8.6 proof 2019 open
190 Combinatorics 8.6 answer — open
191 Geometry 8.6 proof — open
192 Geometry 8.6 proof 2019 open
193 Combinatorics 8.6 answer — open
194 Algebra 8.6 answer — open
195 Number theory 8.6 proof — open
196 Algebra 8.6 answer — open
197 Number theory 8.6 answer — open
198 Algebra 8.6 proof — open
199 Algebra 8.6 proof 2016 open
200 Algebra 8.6 proof — open
201 Algebra 8.6 proof — open
202 Combinatorics 8.6 answer — open
203 Combinatorics 8.6 proof 2020 open
204 Geometry 8.6 proof — open
205 Algebra 8.6 proof — open
206 Combinatorics 8.6 proof — open
207 Geometry 8.6 proof — open
208 Combinatorics 8.7 proof — open
209 Algebra 8.7 proof 2019 open
210 Geometry 8.7 proof — open
211 Number theory 8.7 proof 2016 open
212 Number theory 8.7 proof — open
213 Number theory 8.7 proof 2021 open
214 Number theory 8.7 proof 2016 open
215 Algebra 8.7 proof 2020 open
216 Geometry 8.7 proof — open
217 Number theory 8.7 proof 2019 open
218 Algebra 8.7 answer — open
219 Algebra 8.7 proof — open
220 Geometry 8.7 answer — open
221 Algebra 8.7 answer — open
222 Geometry 8.7 proof 2006 open
223 Geometry 8.7 proof — open
224 Number theory 8.7 proof — open
225 Algebra 8.7 proof 2020 open
226 Geometry 8.7 proof — open
227 Combinatorics 8.7 answer — open
228 Algebra 8.7 answer — open
229 Geometry 8.7 proof 2016 open
230 Number theory 8.7 proof 2011 open
231 Geometry 8.7 proof — open
232 Geometry 8.7 proof — open
233 Number theory 8.7 proof 2007 open
234 Combinatorics 8.7 proof 2007 open
235 Geometry 8.7 proof — open
236 Geometry 8.7 proof — open
237 Number theory 8.7 proof — open
238 Geometry 8.7 proof 2007 open
239 Algebra 8.7 answer — open
240 Geometry 8.7 proof — open
241 Algebra 8.7 proof — open
242 Combinatorics 8.7 proof — open
243 Number theory 8.7 answer — open
244 Algebra 8.7 proof 2019 open
245 Geometry 8.7 proof 2006 open
246 Algebra 8.7 answer — open
247 Algebra 8.7 answer — open
248 Algebra 8.7 proof 2006 open
249 Combinatorics 8.7 proof 2006 open
250 Algebra 8.7 proof 2006 open
251 Algebra 8.7 answer — open
252 Geometry 8.8 proof — open
253 Algebra 8.8 proof — open
254 Algebra 8.8 proof — open
255 Geometry 8.8 proof — open
256 Combinatorics 8.8 answer — open
257 Combinatorics 8.8 proof — open
258 Geometry 8.8 proof 2006 open
259 Geometry 8.8 proof — open
260 Number theory 8.8 proof — open
261 Combinatorics 8.8 proof — open
262 Geometry 8.8 proof 2016 open
263 Combinatorics 8.8 answer — open
264 Combinatorics 8.8 answer — open
265 Algebra 8.8 proof 2021 open
266 Geometry 8.8 proof 2006 open
267 Combinatorics 8.8 proof — open
268 Geometry 8.8 answer — open
269 Algebra 8.8 answer — open
270 Algebra 8.8 proof 2011 open
271 Algebra 8.8 proof — open
272 Algebra 8.8 proof — open
273 Number theory 8.8 proof 2019 open
274 Geometry 8.8 proof 2011 open
275 Geometry 8.8 proof 2016 open
276 Geometry 8.8 proof — open
277 Combinatorics 8.8 proof 2020 open
278 Combinatorics 8.8 proof 2021 open
279 Algebra 8.8 answer — open
280 Number theory 8.8 proof 2019 open
281 Combinatorics 8.8 proof — open
282 Geometry 8.8 proof 2006 open
283 Number theory 8.8 proof — open
284 Number theory 8.8 answer — open
285 Number theory 8.8 answer — open
286 Geometry 8.8 proof 2007 open
287 Geometry 8.8 proof 2021 open
288 Combinatorics 8.8 proof 2016 open
289 Geometry 8.8 proof — open
290 Combinatorics 8.8 proof — open
291 Combinatorics 8.8 proof — open
292 Algebra 8.8 proof — open
293 Geometry 8.8 proof — open
294 Combinatorics 8.8 proof — open
295 Geometry 8.9 proof 2016 open
296 Combinatorics 8.9 answer — open
297 Combinatorics 8.9 proof — open
298 Number theory 8.9 proof — open
299 Geometry 8.9 answer — open
300 Geometry 8.9 proof 2016 open
301 Geometry 8.9 proof — open
302 Combinatorics 8.9 proof — open
303 Geometry 8.9 proof 2016 open
304 Geometry 8.9 proof 2019 open
305 Combinatorics 8.9 answer — open
306 Number theory 8.9 proof 2007 open
307 Combinatorics 8.9 proof — open
308 Algebra 8.9 proof 2019 open
309 Combinatorics 8.9 proof — open
310 Algebra 8.9 proof 2006 open
311 Combinatorics 8.9 answer — open
312 Combinatorics 8.9 proof — open
313 Number theory 8.9 proof 2016 open
314 Geometry 8.9 proof — open
315 Number theory 8.9 proof — open
316 Number theory 8.9 proof — open
317 Algebra 8.9 answer — open
318 Combinatorics 8.9 answer — open
319 Algebra 8.9 proof 2007 open
320 Geometry 8.9 proof 2006 open
321 Number theory 8.9 proof — open
322 Geometry 9.0 proof 2019 open
323 Geometry 9.0 proof — open
324 Number theory 9.0 proof — open
325 Number theory 9.0 proof — open
326 Number theory 9.0 proof — open
327 Algebra 9.0 proof — open
328 Number theory 9.0 proof — open
329 Geometry 9.0 proof 2006 open
330 Number theory 9.0 proof 2011 open
331 Combinatorics 9.0 proof 2019 open
332 Geometry 9.0 proof 2019 open
333 Number theory 9.0 proof — open
334 Algebra 9.0 proof — open
335 Number theory 9.0 proof — open
336 Algebra 9.0 proof — open
337 Geometry 9.0 proof — open
338 Combinatorics 9.0 proof — open
339 Geometry 9.0 proof — open
340 Combinatorics 9.0 proof — open
341 Combinatorics 9.0 proof — open
342 Algebra 9.0 proof — open
343 Algebra 9.0 proof — open
344 Number theory 9.0 proof — open
345 Algebra 9.0 proof — open
346 Algebra 9.0 proof — open
347 Algebra 9.1 proof 2016 open
348 Algebra 9.1 answer — open
349 Combinatorics 9.1 proof 2011 open
350 Combinatorics 9.1 proof — open
351 Algebra 9.1 proof — open
352 Combinatorics 9.1 proof 2006 open
353 Algebra 9.1 proof — open
354 Combinatorics 9.1 proof 2007 open
355 Combinatorics 9.1 proof 2007 open
356 Combinatorics 9.1 answer — open
357 Combinatorics 9.1 answer — open
358 Combinatorics 9.1 answer — open
359 Combinatorics 9.1 proof — open
360 Combinatorics 9.1 proof 2019 open
361 Combinatorics 9.2 proof 2019 open
362 Combinatorics 9.2 proof — open
363 Number theory 9.2 proof — open
364 Algebra 9.2 proof — open
365 Combinatorics 9.2 proof — open
366 Combinatorics 9.2 proof 2011 open
367 Combinatorics 9.3 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.