Maths Olympiad Prep

Library /Irish Mathematical Olympiad

Irish Mathematical Olympiad

351 problems here, rated 4.3 to 7.8 on our scale (AIME to National Olympiad, round 2). 349 of them ask for a proof.

Algebra 125Combinatorics 39Geometry 123Number theory 64
#TopicDiffTypeYear
1 Geometry 4.3 proof — open
2 Algebra 4.3 proof — open
3 Algebra 4.3 proof — open
4 Number theory 4.3 proof — open
5 Geometry 4.3 proof — open
6 Geometry 4.3 proof — open
7 Geometry 4.4 proof — open
8 Algebra 4.4 proof 2014 open
9 Algebra 4.4 proof — open
10 Geometry 4.4 proof — open
11 Geometry 4.4 proof 2014 open
12 Geometry 4.4 proof — open
13 Geometry 4.4 proof — open
14 Geometry 4.5 proof — open
15 Geometry 4.5 proof — open
16 Number theory 4.5 proof — open
17 Geometry 4.5 proof — open
18 Geometry 4.5 proof — open
19 Algebra 4.5 proof — open
20 Number theory 4.5 proof — open
21 Geometry 4.5 proof — open
22 Algebra 4.5 proof — open
23 Algebra 4.5 proof — open
24 Algebra 4.5 proof — open
25 Algebra 4.5 proof — open
26 Number theory 4.5 proof — open
27 Algebra 4.5 proof — open
28 Geometry 4.5 proof — open
29 Algebra 4.5 proof — open
30 Geometry 4.5 proof — open
31 Algebra 4.6 proof — open
32 Algebra 4.6 proof — open
33 Geometry 4.6 proof — open
34 Algebra 4.6 proof — open
35 Geometry 4.6 proof — open
36 Algebra 4.6 proof 2014 open
37 Algebra 4.6 proof — open
38 Algebra 4.6 proof — open
39 Algebra 4.6 proof — open
40 Algebra 4.7 proof — open
41 Algebra 4.7 proof — open
42 Number theory 4.7 proof — open
43 Algebra 4.7 proof — open
44 Number theory 4.7 proof — open
45 Algebra 4.7 proof — open
46 Geometry 4.7 proof 2014 open
47 Geometry 4.7 proof — open
48 Algebra 4.7 proof — open
49 Geometry 4.7 proof 2014 open
50 Algebra 4.7 proof — open
51 Algebra 4.8 proof — open
52 Geometry 4.8 proof — open
53 Number theory 4.8 proof 2014 open
54 Algebra 4.8 proof — open
55 Algebra 4.8 proof — open
56 Algebra 4.8 proof — open
57 Geometry 4.8 proof — open
58 Geometry 4.8 proof — open
59 Geometry 4.8 proof — open
60 Number theory 4.8 proof 2014 open
61 Geometry 4.8 proof — open
62 Number theory 4.8 proof — open
63 Geometry 4.8 proof — open
64 Number theory 4.8 proof — open
65 Algebra 4.9 proof — open
66 Geometry 4.9 proof — open
67 Geometry 4.9 proof — open
68 Geometry 4.9 proof — open
69 Geometry 4.9 proof — open
70 Algebra 4.9 proof — open
71 Combinatorics 5.0 proof — open
72 Algebra 5.0 answer — open
73 Number theory 5.0 proof — open
74 Number theory 5.0 proof — open
75 Algebra 5.0 proof 2014 open
76 Algebra 5.0 proof — open
77 Algebra 5.0 proof — open
78 Number theory 5.0 proof — open
79 Number theory 5.0 proof — open
80 Geometry 5.0 proof — open
81 Geometry 5.0 proof — open
82 Geometry 5.0 proof — open
83 Number theory 5.0 proof — open
84 Geometry 5.0 proof — open
85 Number theory 5.0 proof — open
86 Algebra 5.0 proof — open
87 Geometry 5.1 proof — open
88 Combinatorics 5.1 proof 2014 open
89 Number theory 5.1 proof — open
90 Geometry 5.1 proof — open
91 Algebra 5.1 proof — open
92 Algebra 5.1 proof — open
93 Number theory 5.1 proof — open
94 Algebra 5.1 proof — open
95 Geometry 5.1 proof — open
96 Algebra 5.1 proof — open
97 Algebra 5.1 proof — open
98 Geometry 5.1 proof — open
99 Geometry 5.2 proof — open
100 Algebra 5.2 proof — open
101 Geometry 5.2 proof — open
102 Geometry 5.2 proof — open
103 Geometry 5.2 proof 2014 open
104 Algebra 5.2 proof — open
105 Algebra 5.2 proof — open
106 Geometry 5.2 proof — open
107 Geometry 5.2 proof — open
108 Algebra 5.2 proof — open
109 Algebra 5.2 proof — open
110 Algebra 5.2 proof — open
111 Number theory 5.2 proof — open
112 Algebra 5.2 proof — open
113 Algebra 5.2 proof — open
114 Number theory 5.2 proof — open
115 Number theory 5.2 proof — open
116 Algebra 5.2 proof 2014 open
117 Number theory 5.3 proof — open
118 Algebra 5.3 proof — open
119 Geometry 5.3 proof — open
120 Algebra 5.3 proof — open
121 Geometry 5.3 proof — open
122 Algebra 5.3 proof 2014 open
123 Combinatorics 5.3 proof — open
124 Algebra 5.3 proof 2014 open
125 Number theory 5.3 proof — open
126 Algebra 5.3 proof — open
127 Geometry 5.3 proof — open
128 Geometry 5.3 proof — open
129 Number theory 5.3 proof — open
130 Algebra 5.3 answer — open
131 Algebra 5.3 proof — open
132 Algebra 5.3 proof — open
133 Geometry 5.3 proof — open
134 Combinatorics 5.3 proof — open
135 Geometry 5.4 proof — open
136 Algebra 5.4 proof — open
137 Algebra 5.4 proof — open
138 Algebra 5.4 proof — open
139 Geometry 5.4 proof — open
140 Geometry 5.4 proof — open
141 Geometry 5.4 proof — open
142 Geometry 5.4 proof 2014 open
143 Number theory 5.4 proof — open
144 Geometry 5.4 proof — open
145 Geometry 5.4 proof — open
146 Algebra 5.4 proof — open
147 Algebra 5.4 proof — open
148 Geometry 5.4 proof — open
149 Number theory 5.4 proof — open
150 Geometry 5.4 proof — open
151 Geometry 5.4 proof — open
152 Algebra 5.4 proof — open
153 Algebra 5.4 proof — open
154 Algebra 5.4 proof — open
155 Geometry 5.4 proof — open
156 Number theory 5.4 proof — open
157 Algebra 5.4 proof — open
158 Geometry 5.4 proof — open
159 Geometry 5.5 proof — open
160 Geometry 5.5 proof — open
161 Geometry 5.5 proof — open
162 Geometry 5.5 proof — open
163 Combinatorics 5.5 proof — open
164 Number theory 5.5 proof — open
165 Geometry 5.5 proof — open
166 Geometry 5.5 proof — open
167 Algebra 5.5 proof — open
168 Geometry 5.5 proof 2014 open
169 Algebra 5.5 proof — open
170 Geometry 5.5 proof — open
171 Geometry 5.5 proof — open
172 Geometry 5.5 proof — open
173 Number theory 5.5 proof — open
174 Geometry 5.5 proof — open
175 Algebra 5.5 proof — open
176 Algebra 5.6 proof — open
177 Combinatorics 5.6 proof — open
178 Geometry 5.6 proof — open
179 Algebra 5.6 proof — open
180 Geometry 5.6 proof — open
181 Algebra 5.6 proof 2014 open
182 Geometry 5.6 proof — open
183 Geometry 5.6 proof — open
184 Number theory 5.6 proof — open
185 Algebra 5.6 proof — open
186 Number theory 5.6 proof — open
187 Algebra 5.6 proof — open
188 Number theory 5.6 proof — open
189 Number theory 5.6 proof — open
190 Number theory 5.6 proof — open
191 Combinatorics 5.6 proof — open
192 Number theory 5.6 proof — open
193 Algebra 5.6 proof — open
194 Geometry 5.6 proof — open
195 Algebra 5.6 proof — open
196 Number theory 5.7 proof — open
197 Algebra 5.7 proof 2014 open
198 Geometry 5.7 proof — open
199 Number theory 5.7 proof — open
200 Algebra 5.7 proof — open
201 Algebra 5.7 proof — open
202 Number theory 5.7 proof — open
203 Geometry 5.7 proof — open
204 Algebra 5.7 proof — open
205 Geometry 5.7 proof — open
206 Geometry 5.7 proof — open
207 Combinatorics 5.7 proof 2014 open
208 Geometry 5.7 proof — open
209 Algebra 5.7 proof — open
210 Combinatorics 5.7 proof — open
211 Number theory 5.7 proof — open
212 Geometry 5.7 proof — open
213 Geometry 5.7 proof — open
214 Number theory 5.7 proof — open
215 Geometry 5.8 proof — open
216 Number theory 5.8 proof — open
217 Number theory 5.8 proof — open
218 Geometry 5.8 proof — open
219 Algebra 5.8 proof — open
220 Geometry 5.8 proof — open
221 Number theory 5.8 proof — open
222 Geometry 5.8 proof — open
223 Combinatorics 5.8 proof — open
224 Number theory 5.8 proof — open
225 Combinatorics 5.8 proof — open
226 Number theory 5.8 proof — open
227 Number theory 5.8 proof — open
228 Geometry 5.8 proof — open
229 Algebra 5.8 proof — open
230 Algebra 5.8 proof 2014 open
231 Combinatorics 5.8 proof — open
232 Geometry 5.9 proof — open
233 Geometry 5.9 proof — open
234 Algebra 5.9 proof — open
235 Geometry 5.9 proof — open
236 Geometry 5.9 proof — open
237 Algebra 5.9 proof — open
238 Geometry 5.9 proof — open
239 Algebra 5.9 proof — open
240 Algebra 5.9 proof — open
241 Algebra 5.9 proof — open
242 Geometry 5.9 proof — open
243 Algebra 5.9 proof — open
244 Number theory 5.9 proof — open
245 Algebra 5.9 proof — open
246 Algebra 5.9 proof — open
247 Combinatorics 5.9 proof — open
248 Algebra 5.9 proof — open
249 Geometry 5.9 proof — open
250 Geometry 5.9 proof — open
251 Number theory 6.0 proof — open
252 Number theory 6.0 proof — open
253 Algebra 6.0 proof — open
254 Geometry 6.0 proof — open
255 Number theory 6.0 proof 2014 open
256 Geometry 6.0 proof — open
257 Algebra 6.0 proof — open
258 Algebra 6.0 proof — open
259 Number theory 6.0 proof — open
260 Combinatorics 6.0 proof — open
261 Geometry 6.0 proof — open
262 Number theory 6.0 proof — open
263 Algebra 6.0 proof — open
264 Algebra 6.0 proof — open
265 Combinatorics 6.1 proof — open
266 Algebra 6.1 proof — open
267 Algebra 6.1 proof — open
268 Algebra 6.1 proof — open
269 Geometry 6.1 proof — open
270 Algebra 6.1 proof — open
271 Geometry 6.1 proof — open
272 Algebra 6.1 proof — open
273 Algebra 6.1 proof — open
274 Algebra 6.1 proof — open
275 Geometry 6.1 proof — open
276 Algebra 6.1 proof — open
277 Algebra 6.1 proof — open
278 Number theory 6.2 proof — open
279 Number theory 6.2 proof — open
280 Combinatorics 6.3 proof — open
281 Geometry 6.3 proof — open
282 Geometry 6.3 proof — open
283 Geometry 6.3 proof — open
284 Geometry 6.3 proof — open
285 Geometry 6.3 proof — open
286 Algebra 6.3 proof — open
287 Algebra 6.3 proof — open
288 Geometry 6.4 proof — open
289 Geometry 6.4 proof — open
290 Combinatorics 6.4 proof — open
291 Combinatorics 6.4 proof — open
292 Algebra 6.4 proof — open
293 Number theory 6.4 proof — open
294 Geometry 6.5 proof — open
295 Geometry 6.5 proof — open
296 Algebra 6.5 proof — open
297 Algebra 6.5 proof — open
298 Algebra 6.5 proof — open
299 Number theory 6.5 proof — open
300 Combinatorics 6.5 proof — open
301 Geometry 6.5 proof — open
302 Geometry 6.5 proof — open
303 Algebra 6.6 proof — open
304 Combinatorics 6.6 proof — open
305 Algebra 6.6 proof — open
306 Combinatorics 6.6 proof — open
307 Combinatorics 6.6 proof — open
308 Algebra 6.6 proof — open
309 Number theory 6.6 proof — open
310 Algebra 6.7 proof — open
311 Geometry 6.7 proof — open
312 Combinatorics 6.7 proof — open
313 Algebra 6.7 proof — open
314 Combinatorics 6.7 proof — open
315 Algebra 6.7 proof — open
316 Algebra 6.8 proof — open
317 Combinatorics 6.8 proof — open
318 Geometry 6.8 proof — open
319 Combinatorics 6.8 proof — open
320 Combinatorics 6.9 proof — open
321 Number theory 6.9 proof — open
322 Algebra 6.9 proof — open
323 Geometry 6.9 proof — open
324 Number theory 6.9 proof — open
325 Geometry 6.9 proof — open
326 Combinatorics 6.9 proof — open
327 Geometry 6.9 proof — open
328 Number theory 7.0 proof — open
329 Combinatorics 7.0 proof — open
330 Combinatorics 7.0 proof — open
331 Combinatorics 7.1 proof — open
332 Number theory 7.1 proof — open
333 Geometry 7.1 proof — open
334 Combinatorics 7.2 proof — open
335 Combinatorics 7.2 proof — open
336 Number theory 7.2 proof — open
337 Combinatorics 7.2 proof — open
338 Geometry 7.2 proof — open
339 Combinatorics 7.2 proof — open
340 Algebra 7.3 proof — open
341 Number theory 7.3 proof — open
342 Algebra 7.3 proof — open
343 Combinatorics 7.3 proof — open
344 Number theory 7.4 proof — open
345 Algebra 7.4 proof — open
346 Geometry 7.6 proof — open
347 Algebra 7.6 proof — open
348 Geometry 7.6 proof — open
349 Combinatorics 7.7 proof — open
350 Combinatorics 7.7 proof — open
351 Combinatorics 7.8 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.