Library /Harvard-MIT Mathematics Tournament

Harvard-MIT Mathematics Tournament

352 problems here, rated 3.6 to 6 on our scale (AMC 10/12 to National Olympiad). 291 of them ask for a proof.

Algebra 95Combinatorics 95Geometry 128Number theory 34

#	Topic	Diff	Type	Year
1	Geometry	3.6	answer	—	open
2	Geometry	3.7	answer	—	open
3	Number theory	3.9	answer	—	open
4	Geometry	4.0	answer	—	open
5	Number theory	4.1	answer	—	open
6	Algebra	4.1	answer	—	open
7	Geometry	4.1	proof	—	open
8	Algebra	4.1	answer	—	open
9	Geometry	4.1	answer	—	open
10	Number theory	4.1	answer	—	open
11	Number theory	4.1	answer	—	open
12	Geometry	4.1	answer	—	open
13	Algebra	4.1	answer	—	open
14	Geometry	4.2	answer	—	open
15	Algebra	4.2	answer	—	open
16	Algebra	4.2	answer	—	open
17	Algebra	4.2	answer	—	open
18	Geometry	4.3	answer	—	open
19	Combinatorics	4.3	answer	—	open
20	Algebra	4.3	answer	—	open
21	Geometry	4.3	answer	—	open
22	Geometry	4.3	answer	—	open
23	Combinatorics	4.3	answer	—	open
24	Algebra	4.3	answer	—	open
25	Algebra	4.3	answer	—	open
26	Algebra	4.3	answer	—	open
27	Combinatorics	4.3	answer	—	open
28	Geometry	4.3	answer	—	open
29	Combinatorics	4.4	answer	—	open
30	Number theory	4.4	answer	—	open
31	Algebra	4.4	proof	—	open
32	Geometry	4.4	answer	—	open
33	Algebra	4.4	proof	—	open
34	Combinatorics	4.4	answer	—	open
35	Geometry	4.4	answer	—	open
36	Combinatorics	4.4	answer	—	open
37	Algebra	4.4	proof	—	open
38	Combinatorics	4.4	answer	—	open
39	Geometry	4.4	answer	—	open
40	Combinatorics	4.4	answer	—	open
41	Geometry	4.4	answer	—	open
42	Geometry	4.4	proof	—	open
43	Number theory	4.4	proof	—	open
44	Combinatorics	4.5	proof	—	open
45	Algebra	4.5	answer	—	open
46	Algebra	4.5	answer	—	open
47	Algebra	4.5	answer	—	open
48	Combinatorics	4.5	answer	—	open
49	Geometry	4.5	proof	—	open
50	Algebra	4.5	answer	—	open
51	Geometry	4.5	proof	—	open
52	Algebra	4.5	proof	—	open
53	Geometry	4.6	answer	—	open
54	Algebra	4.6	proof	—	open
55	Geometry	4.6	proof	—	open
56	Number theory	4.6	proof	—	open
57	Algebra	4.6	answer	—	open
58	Geometry	4.6	proof	—	open
59	Number theory	4.6	proof	—	open
60	Algebra	4.6	proof	—	open
61	Geometry	4.6	proof	—	open
62	Combinatorics	4.6	proof	—	open
63	Geometry	4.6	proof	—	open
64	Number theory	4.6	proof	—	open
65	Geometry	4.6	proof	—	open
66	Geometry	4.6	proof	—	open
67	Number theory	4.7	proof	—	open
68	Geometry	4.7	proof	—	open
69	Algebra	4.7	proof	—	open
70	Geometry	4.7	proof	—	open
71	Geometry	4.7	answer	—	open
72	Geometry	4.7	proof	—	open
73	Combinatorics	4.7	proof	—	open
74	Number theory	4.7	proof	—	open
75	Geometry	4.7	proof	—	open
76	Algebra	4.7	proof	—	open
77	Geometry	4.7	proof	—	open
78	Geometry	4.7	proof	—	open
79	Geometry	4.8	proof	—	open
80	Geometry	4.8	proof	—	open
81	Combinatorics	4.8	answer	—	open
82	Algebra	4.8	proof	—	open
83	Combinatorics	4.8	proof	—	open
84	Geometry	4.8	proof	—	open
85	Number theory	4.8	proof	—	open
86	Geometry	4.8	answer	—	open
87	Geometry	4.8	proof	—	open
88	Geometry	4.8	proof	—	open
89	Algebra	4.8	answer	—	open
90	Combinatorics	4.8	proof	—	open
91	Geometry	4.8	answer	—	open
92	Combinatorics	4.8	proof	—	open
93	Number theory	4.9	proof	—	open
94	Geometry	4.9	proof	—	open
95	Geometry	4.9	proof	—	open
96	Geometry	4.9	proof	—	open
97	Geometry	4.9	proof	—	open
98	Algebra	4.9	proof	—	open
99	Geometry	4.9	proof	—	open
100	Algebra	4.9	proof	—	open
101	Algebra	4.9	proof	—	open
102	Algebra	4.9	proof	—	open
103	Geometry	4.9	proof	—	open
104	Geometry	4.9	proof	—	open
105	Geometry	4.9	answer	—	open
106	Algebra	4.9	proof	—	open
107	Geometry	4.9	proof	—	open
108	Algebra	4.9	proof	—	open
109	Geometry	4.9	proof	—	open
110	Combinatorics	4.9	proof	—	open
111	Algebra	4.9	answer	—	open
112	Geometry	4.9	proof	—	open
113	Algebra	4.9	proof	—	open
114	Algebra	4.9	proof	—	open
115	Geometry	4.9	proof	—	open
116	Geometry	4.9	proof	—	open
117	Geometry	4.9	proof	—	open
118	Geometry	4.9	proof	—	open
119	Geometry	4.9	proof	—	open
120	Combinatorics	4.9	answer	—	open
121	Combinatorics	4.9	answer	—	open
122	Geometry	4.9	proof	—	open
123	Algebra	5.0	proof	—	open
124	Geometry	5.0	proof	—	open
125	Algebra	5.0	proof	—	open
126	Geometry	5.0	proof	—	open
127	Geometry	5.0	proof	—	open
128	Algebra	5.0	proof	—	open
129	Geometry	5.0	proof	—	open
130	Combinatorics	5.0	answer	—	open
131	Combinatorics	5.0	answer	—	open
132	Algebra	5.0	proof	—	open
133	Algebra	5.0	proof	—	open
134	Geometry	5.0	proof	—	open
135	Combinatorics	5.0	proof	—	open
136	Algebra	5.0	proof	—	open
137	Geometry	5.0	proof	—	open
138	Geometry	5.0	proof	—	open
139	Geometry	5.0	proof	—	open
140	Algebra	5.0	answer	—	open
141	Geometry	5.0	proof	—	open
142	Number theory	5.0	proof	—	open
143	Geometry	5.0	proof	—	open
144	Algebra	5.0	proof	—	open
145	Algebra	5.0	proof	—	open
146	Algebra	5.0	proof	—	open
147	Geometry	5.0	proof	—	open
148	Combinatorics	5.0	answer	—	open
149	Algebra	5.0	proof	—	open
150	Combinatorics	5.0	proof	—	open
151	Geometry	5.0	proof	—	open
152	Algebra	5.0	proof	—	open
153	Algebra	5.0	proof	—	open
154	Algebra	5.0	proof	—	open
155	Geometry	5.0	proof	—	open
156	Algebra	5.0	proof	—	open
157	Combinatorics	5.0	answer	—	open
158	Algebra	5.0	proof	—	open
159	Geometry	5.0	proof	—	open
160	Geometry	5.1	proof	—	open
161	Combinatorics	5.1	proof	—	open
162	Algebra	5.1	proof	—	open
163	Algebra	5.1	proof	—	open
164	Geometry	5.1	proof	—	open
165	Geometry	5.1	proof	—	open
166	Algebra	5.1	proof	—	open
167	Combinatorics	5.1	proof	—	open
168	Algebra	5.1	proof	—	open
169	Algebra	5.1	proof	—	open
170	Algebra	5.1	proof	—	open
171	Combinatorics	5.1	proof	—	open
172	Algebra	5.1	proof	—	open
173	Algebra	5.1	proof	—	open
174	Number theory	5.1	proof	—	open
175	Algebra	5.1	proof	—	open
176	Algebra	5.1	proof	—	open
177	Combinatorics	5.1	proof	—	open
178	Combinatorics	5.1	proof	—	open
179	Number theory	5.1	proof	—	open
180	Number theory	5.1	proof	—	open
181	Geometry	5.1	proof	—	open
182	Geometry	5.1	proof	—	open
183	Combinatorics	5.1	proof	—	open
184	Algebra	5.1	proof	—	open
185	Combinatorics	5.1	proof	—	open
186	Algebra	5.1	proof	—	open
187	Number theory	5.1	proof	—	open
188	Combinatorics	5.1	proof	—	open
189	Combinatorics	5.1	proof	—	open
190	Geometry	5.1	proof	—	open
191	Geometry	5.1	proof	—	open
192	Combinatorics	5.1	proof	—	open
193	Geometry	5.1	proof	—	open
194	Geometry	5.1	proof	—	open
195	Number theory	5.1	proof	—	open
196	Geometry	5.1	proof	—	open
197	Combinatorics	5.1	proof	—	open
198	Algebra	5.2	proof	—	open
199	Geometry	5.2	proof	—	open
200	Combinatorics	5.2	proof	—	open
201	Number theory	5.2	answer	—	open
202	Algebra	5.2	answer	—	open
203	Combinatorics	5.2	proof	—	open
204	Algebra	5.2	proof	—	open
205	Combinatorics	5.2	proof	—	open
206	Combinatorics	5.2	proof	—	open
207	Algebra	5.2	proof	—	open
208	Combinatorics	5.2	proof	—	open
209	Geometry	5.2	proof	—	open
210	Geometry	5.2	proof	—	open
211	Combinatorics	5.2	proof	—	open
212	Geometry	5.2	proof	—	open
213	Geometry	5.2	proof	—	open
214	Combinatorics	5.2	proof	—	open
215	Geometry	5.2	proof	—	open
216	Geometry	5.2	proof	—	open
217	Combinatorics	5.2	proof	—	open
218	Algebra	5.2	proof	—	open
219	Geometry	5.2	proof	—	open
220	Algebra	5.2	proof	—	open
221	Combinatorics	5.2	proof	—	open
222	Algebra	5.2	proof	—	open
223	Number theory	5.2	proof	—	open
224	Combinatorics	5.2	proof	—	open
225	Algebra	5.3	proof	—	open
226	Combinatorics	5.3	proof	—	open
227	Geometry	5.3	proof	—	open
228	Combinatorics	5.3	proof	—	open
229	Combinatorics	5.3	proof	—	open
230	Number theory	5.3	proof	—	open
231	Combinatorics	5.3	proof	—	open
232	Algebra	5.3	proof	—	open
233	Geometry	5.3	proof	—	open
234	Number theory	5.3	proof	—	open
235	Combinatorics	5.3	proof	—	open
236	Algebra	5.3	proof	—	open
237	Number theory	5.3	proof	—	open
238	Combinatorics	5.3	proof	—	open
239	Combinatorics	5.3	answer	—	open
240	Algebra	5.3	proof	—	open
241	Combinatorics	5.3	proof	—	open
242	Combinatorics	5.3	proof	—	open
243	Algebra	5.3	proof	—	open
244	Algebra	5.3	proof	—	open
245	Combinatorics	5.3	proof	—	open
246	Algebra	5.3	proof	—	open
247	Algebra	5.4	proof	—	open
248	Geometry	5.4	proof	—	open
249	Combinatorics	5.4	proof	—	open
250	Geometry	5.4	proof	—	open
251	Geometry	5.4	proof	—	open
252	Number theory	5.4	proof	—	open
253	Geometry	5.4	proof	—	open
254	Algebra	5.4	proof	—	open
255	Algebra	5.4	proof	—	open
256	Geometry	5.4	proof	—	open
257	Number theory	5.4	proof	—	open
258	Geometry	5.4	proof	—	open
259	Number theory	5.4	proof	—	open
260	Combinatorics	5.4	proof	—	open
261	Geometry	5.4	proof	—	open
262	Combinatorics	5.4	proof	—	open
263	Combinatorics	5.4	proof	—	open
264	Combinatorics	5.5	proof	—	open
265	Geometry	5.5	proof	—	open
266	Algebra	5.5	proof	—	open
267	Algebra	5.5	proof	—	open
268	Combinatorics	5.5	proof	—	open
269	Algebra	5.5	proof	—	open
270	Geometry	5.5	proof	—	open
271	Number theory	5.5	proof	—	open
272	Geometry	5.5	proof	—	open
273	Geometry	5.5	proof	—	open
274	Geometry	5.5	proof	—	open
275	Geometry	5.5	proof	—	open
276	Geometry	5.5	proof	—	open
277	Geometry	5.5	proof	—	open
278	Geometry	5.5	proof	—	open
279	Combinatorics	5.5	proof	—	open
280	Geometry	5.5	proof	—	open
281	Geometry	5.5	proof	—	open
282	Algebra	5.5	proof	—	open
283	Geometry	5.5	proof	—	open
284	Combinatorics	5.5	proof	—	open
285	Geometry	5.5	proof	—	open
286	Geometry	5.5	proof	—	open
287	Geometry	5.5	proof	—	open
288	Geometry	5.5	proof	—	open
289	Geometry	5.5	proof	—	open
290	Algebra	5.5	proof	—	open
291	Number theory	5.5	proof	—	open
292	Combinatorics	5.5	proof	—	open
293	Number theory	5.6	proof	—	open
294	Algebra	5.6	proof	—	open
295	Combinatorics	5.6	proof	—	open
296	Geometry	5.6	proof	—	open
297	Geometry	5.6	proof	—	open
298	Number theory	5.6	proof	—	open
299	Geometry	5.6	proof	—	open
300	Combinatorics	5.6	proof	—	open
301	Combinatorics	5.6	proof	—	open
302	Geometry	5.6	proof	—	open
303	Combinatorics	5.6	proof	—	open
304	Combinatorics	5.6	proof	—	open
305	Combinatorics	5.7	proof	—	open
306	Algebra	5.7	proof	—	open
307	Algebra	5.7	proof	—	open
308	Combinatorics	5.7	proof	—	open
309	Combinatorics	5.7	proof	—	open
310	Combinatorics	5.7	proof	—	open
311	Algebra	5.7	proof	—	open
312	Geometry	5.7	proof	—	open
313	Geometry	5.7	proof	—	open
314	Combinatorics	5.7	proof	—	open
315	Geometry	5.7	proof	—	open
316	Algebra	5.7	proof	—	open
317	Geometry	5.7	proof	—	open
318	Combinatorics	5.7	proof	—	open
319	Combinatorics	5.7	proof	—	open
320	Combinatorics	5.7	proof	—	open
321	Combinatorics	5.7	proof	—	open
322	Combinatorics	5.7	proof	—	open
323	Combinatorics	5.7	proof	—	open
324	Geometry	5.7	proof	—	open
325	Algebra	5.8	proof	—	open
326	Combinatorics	5.8	proof	—	open
327	Algebra	5.8	proof	—	open
328	Number theory	5.8	proof	—	open
329	Geometry	5.8	proof	—	open
330	Combinatorics	5.8	proof	—	open
331	Geometry	5.8	proof	—	open
332	Combinatorics	5.8	proof	—	open
333	Combinatorics	5.8	proof	—	open
334	Combinatorics	5.8	proof	—	open
335	Algebra	5.8	proof	—	open
336	Combinatorics	5.8	proof	—	open
337	Algebra	5.9	proof	—	open
338	Number theory	5.9	proof	—	open
339	Combinatorics	5.9	proof	—	open
340	Combinatorics	5.9	proof	—	open
341	Number theory	5.9	proof	—	open
342	Algebra	6.0	proof	—	open
343	Algebra	6.0	proof	—	open
344	Geometry	6.0	proof	—	open
345	Combinatorics	6.0	proof	—	open
346	Combinatorics	6.0	proof	—	open
347	Combinatorics	6.0	proof	—	open
348	Geometry	6.0	proof	—	open
349	Combinatorics	6.0	proof	—	open
350	Combinatorics	6.0	proof	—	open
351	Geometry	6.0	proof	—	open
352	Combinatorics	6.0	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.