Library /Harvard-MIT Mathematics Tournament

Harvard-MIT Mathematics Tournament

377 problems here, rated 3.6 to 6 on our scale (AMC 10/12 to National Olympiad). 312 of them ask for a proof.

Algebra 97Combinatorics 110Geometry 133Number theory 37

#	Topic	Diff	Type	Year
1	Geometry	3.6	answer	—	open
2	Geometry	3.6	answer	—	open
3	Geometry	3.7	answer	—	open
4	Number theory	3.9	answer	—	open
5	Combinatorics	4.0	proof	—	open
6	Geometry	4.0	answer	—	open
7	Number theory	4.1	answer	—	open
8	Algebra	4.1	answer	—	open
9	Geometry	4.1	proof	—	open
10	Algebra	4.1	answer	—	open
11	Geometry	4.1	answer	—	open
12	Number theory	4.1	answer	—	open
13	Number theory	4.1	answer	—	open
14	Geometry	4.1	answer	—	open
15	Algebra	4.1	answer	—	open
16	Geometry	4.2	answer	—	open
17	Algebra	4.2	answer	—	open
18	Algebra	4.2	answer	—	open
19	Algebra	4.2	answer	—	open
20	Geometry	4.3	answer	—	open
21	Combinatorics	4.3	answer	—	open
22	Algebra	4.3	answer	—	open
23	Geometry	4.3	answer	—	open
24	Geometry	4.3	answer	—	open
25	Combinatorics	4.3	answer	—	open
26	Algebra	4.3	answer	—	open
27	Algebra	4.3	answer	—	open
28	Algebra	4.3	answer	—	open
29	Combinatorics	4.3	answer	—	open
30	Geometry	4.3	answer	—	open
31	Combinatorics	4.4	answer	—	open
32	Number theory	4.4	answer	—	open
33	Geometry	4.4	proof	—	open
34	Combinatorics	4.4	answer	—	open
35	Algebra	4.4	proof	—	open
36	Geometry	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	Combinatorics	4.4	answer	—	open
42	Algebra	4.4	proof	—	open
43	Combinatorics	4.4	answer	—	open
44	Geometry	4.4	answer	—	open
45	Combinatorics	4.4	answer	—	open
46	Geometry	4.4	answer	—	open
47	Geometry	4.4	proof	—	open
48	Number theory	4.4	proof	—	open
49	Combinatorics	4.5	proof	—	open
50	Algebra	4.5	answer	—	open
51	Algebra	4.5	answer	—	open
52	Algebra	4.5	answer	—	open
53	Combinatorics	4.5	answer	—	open
54	Geometry	4.5	proof	—	open
55	Algebra	4.5	answer	—	open
56	Geometry	4.5	proof	—	open
57	Algebra	4.5	proof	—	open
58	Geometry	4.6	answer	—	open
59	Algebra	4.6	proof	—	open
60	Geometry	4.6	proof	—	open
61	Number theory	4.6	proof	—	open
62	Algebra	4.6	answer	—	open
63	Geometry	4.6	proof	—	open
64	Number theory	4.6	proof	—	open
65	Geometry	4.6	proof	—	open
66	Algebra	4.6	proof	—	open
67	Geometry	4.6	proof	—	open
68	Combinatorics	4.6	proof	—	open
69	Geometry	4.6	proof	—	open
70	Number theory	4.6	proof	—	open
71	Geometry	4.6	proof	—	open
72	Geometry	4.6	proof	—	open
73	Algebra	4.7	proof	—	open
74	Number theory	4.7	proof	—	open
75	Number theory	4.7	proof	—	open
76	Geometry	4.7	proof	—	open
77	Algebra	4.7	proof	—	open
78	Geometry	4.7	proof	—	open
79	Geometry	4.7	answer	—	open
80	Geometry	4.7	proof	—	open
81	Combinatorics	4.7	proof	—	open
82	Number theory	4.7	proof	—	open
83	Geometry	4.7	proof	—	open
84	Algebra	4.7	proof	—	open
85	Geometry	4.7	proof	—	open
86	Geometry	4.7	proof	—	open
87	Geometry	4.8	proof	—	open
88	Geometry	4.8	proof	—	open
89	Combinatorics	4.8	answer	—	open
90	Algebra	4.8	proof	—	open
91	Combinatorics	4.8	proof	—	open
92	Geometry	4.8	proof	—	open
93	Number theory	4.8	proof	—	open
94	Geometry	4.8	answer	—	open
95	Geometry	4.8	proof	—	open
96	Geometry	4.8	proof	—	open
97	Combinatorics	4.8	proof	—	open
98	Algebra	4.8	answer	—	open
99	Combinatorics	4.8	proof	—	open
100	Geometry	4.8	answer	—	open
101	Algebra	4.8	proof	—	open
102	Number theory	4.8	proof	—	open
103	Combinatorics	4.8	proof	—	open
104	Number theory	4.9	proof	—	open
105	Geometry	4.9	proof	—	open
106	Geometry	4.9	proof	—	open
107	Geometry	4.9	proof	—	open
108	Geometry	4.9	proof	—	open
109	Algebra	4.9	proof	—	open
110	Geometry	4.9	proof	—	open
111	Algebra	4.9	proof	—	open
112	Algebra	4.9	proof	—	open
113	Algebra	4.9	proof	—	open
114	Geometry	4.9	proof	—	open
115	Geometry	4.9	proof	—	open
116	Geometry	4.9	answer	—	open
117	Algebra	4.9	proof	—	open
118	Geometry	4.9	proof	—	open
119	Algebra	4.9	proof	—	open
120	Geometry	4.9	proof	—	open
121	Combinatorics	4.9	proof	—	open
122	Geometry	4.9	proof	—	open
123	Algebra	4.9	answer	—	open
124	Geometry	4.9	proof	—	open
125	Algebra	4.9	proof	—	open
126	Algebra	4.9	proof	—	open
127	Geometry	4.9	proof	—	open
128	Geometry	4.9	proof	—	open
129	Geometry	4.9	proof	—	open
130	Geometry	4.9	proof	—	open
131	Geometry	4.9	proof	—	open
132	Geometry	4.9	answer	—	open
133	Combinatorics	4.9	answer	—	open
134	Combinatorics	4.9	answer	—	open
135	Geometry	4.9	proof	—	open
136	Algebra	5.0	proof	—	open
137	Geometry	5.0	proof	—	open
138	Algebra	5.0	proof	—	open
139	Geometry	5.0	proof	—	open
140	Geometry	5.0	proof	—	open
141	Algebra	5.0	proof	—	open
142	Geometry	5.0	proof	—	open
143	Combinatorics	5.0	answer	—	open
144	Combinatorics	5.0	answer	—	open
145	Algebra	5.0	proof	—	open
146	Algebra	5.0	proof	—	open
147	Geometry	5.0	proof	—	open
148	Combinatorics	5.0	proof	—	open
149	Algebra	5.0	proof	—	open
150	Geometry	5.0	proof	—	open
151	Geometry	5.0	proof	—	open
152	Geometry	5.0	proof	—	open
153	Algebra	5.0	answer	—	open
154	Geometry	5.0	proof	—	open
155	Number theory	5.0	proof	—	open
156	Geometry	5.0	proof	—	open
157	Algebra	5.0	proof	—	open
158	Number theory	5.0	proof	—	open
159	Algebra	5.0	proof	—	open
160	Algebra	5.0	proof	—	open
161	Geometry	5.0	proof	—	open
162	Combinatorics	5.0	answer	—	open
163	Algebra	5.0	proof	—	open
164	Combinatorics	5.0	proof	—	open
165	Geometry	5.0	proof	—	open
166	Algebra	5.0	proof	—	open
167	Algebra	5.0	proof	—	open
168	Algebra	5.0	proof	—	open
169	Geometry	5.0	proof	—	open
170	Algebra	5.0	proof	—	open
171	Combinatorics	5.0	answer	—	open
172	Algebra	5.0	proof	—	open
173	Combinatorics	5.0	proof	—	open
174	Geometry	5.0	proof	—	open
175	Geometry	5.1	proof	—	open
176	Combinatorics	5.1	proof	—	open
177	Algebra	5.1	proof	—	open
178	Algebra	5.1	proof	—	open
179	Geometry	5.1	proof	—	open
180	Geometry	5.1	proof	—	open
181	Algebra	5.1	proof	—	open
182	Combinatorics	5.1	proof	—	open
183	Algebra	5.1	proof	—	open
184	Algebra	5.1	proof	—	open
185	Algebra	5.1	proof	—	open
186	Combinatorics	5.1	proof	—	open
187	Algebra	5.1	proof	—	open
188	Algebra	5.1	proof	—	open
189	Number theory	5.1	proof	—	open
190	Algebra	5.1	proof	—	open
191	Algebra	5.1	proof	—	open
192	Combinatorics	5.1	proof	—	open
193	Combinatorics	5.1	proof	—	open
194	Number theory	5.1	proof	—	open
195	Number theory	5.1	proof	—	open
196	Geometry	5.1	proof	—	open
197	Geometry	5.1	proof	—	open
198	Combinatorics	5.1	proof	—	open
199	Algebra	5.1	proof	—	open
200	Combinatorics	5.1	proof	—	open
201	Algebra	5.1	proof	—	open
202	Number theory	5.1	proof	—	open
203	Combinatorics	5.1	proof	—	open
204	Combinatorics	5.1	proof	—	open
205	Geometry	5.1	proof	—	open
206	Geometry	5.1	proof	—	open
207	Combinatorics	5.1	proof	—	open
208	Geometry	5.1	proof	—	open
209	Geometry	5.1	proof	—	open
210	Number theory	5.1	proof	—	open
211	Geometry	5.1	proof	—	open
212	Combinatorics	5.1	proof	—	open
213	Algebra	5.2	proof	—	open
214	Geometry	5.2	proof	—	open
215	Combinatorics	5.2	proof	—	open
216	Number theory	5.2	answer	—	open
217	Algebra	5.2	answer	—	open
218	Combinatorics	5.2	proof	—	open
219	Algebra	5.2	proof	—	open
220	Combinatorics	5.2	proof	—	open
221	Combinatorics	5.2	proof	—	open
222	Combinatorics	5.2	proof	—	open
223	Combinatorics	5.2	proof	—	open
224	Combinatorics	5.2	proof	—	open
225	Algebra	5.2	proof	—	open
226	Combinatorics	5.2	proof	—	open
227	Geometry	5.2	proof	—	open
228	Geometry	5.2	proof	—	open
229	Combinatorics	5.2	proof	—	open
230	Geometry	5.2	proof	—	open
231	Geometry	5.2	proof	—	open
232	Combinatorics	5.2	proof	—	open
233	Geometry	5.2	proof	—	open
234	Geometry	5.2	proof	—	open
235	Combinatorics	5.2	proof	—	open
236	Combinatorics	5.2	proof	—	open
237	Algebra	5.2	proof	—	open
238	Geometry	5.2	proof	—	open
239	Algebra	5.2	proof	—	open
240	Combinatorics	5.2	proof	—	open
241	Algebra	5.2	proof	—	open
242	Number theory	5.2	proof	—	open
243	Combinatorics	5.2	proof	—	open
244	Algebra	5.3	proof	—	open
245	Combinatorics	5.3	proof	—	open
246	Combinatorics	5.3	proof	—	open
247	Geometry	5.3	proof	—	open
248	Combinatorics	5.3	proof	—	open
249	Combinatorics	5.3	proof	—	open
250	Number theory	5.3	proof	—	open
251	Combinatorics	5.3	proof	—	open
252	Algebra	5.3	proof	—	open
253	Geometry	5.3	proof	—	open
254	Number theory	5.3	proof	—	open
255	Combinatorics	5.3	proof	—	open
256	Algebra	5.3	proof	—	open
257	Number theory	5.3	proof	—	open
258	Combinatorics	5.3	proof	—	open
259	Combinatorics	5.3	answer	—	open
260	Algebra	5.3	proof	—	open
261	Combinatorics	5.3	proof	—	open
262	Combinatorics	5.3	proof	—	open
263	Algebra	5.3	proof	—	open
264	Algebra	5.3	proof	—	open
265	Combinatorics	5.3	proof	—	open
266	Algebra	5.3	proof	—	open
267	Algebra	5.4	proof	—	open
268	Geometry	5.4	proof	—	open
269	Combinatorics	5.4	proof	—	open
270	Geometry	5.4	proof	—	open
271	Combinatorics	5.4	proof	—	open
272	Geometry	5.4	proof	—	open
273	Number theory	5.4	proof	—	open
274	Geometry	5.4	proof	—	open
275	Algebra	5.4	proof	—	open
276	Algebra	5.4	proof	—	open
277	Geometry	5.4	proof	—	open
278	Number theory	5.4	proof	—	open
279	Geometry	5.4	proof	—	open
280	Number theory	5.4	proof	—	open
281	Combinatorics	5.4	proof	—	open
282	Geometry	5.4	proof	—	open
283	Combinatorics	5.4	proof	—	open
284	Combinatorics	5.4	proof	—	open
285	Combinatorics	5.4	proof	—	open
286	Combinatorics	5.5	proof	—	open
287	Geometry	5.5	proof	—	open
288	Algebra	5.5	proof	—	open
289	Algebra	5.5	proof	—	open
290	Combinatorics	5.5	proof	—	open
291	Algebra	5.5	proof	—	open
292	Geometry	5.5	proof	—	open
293	Number theory	5.5	proof	—	open
294	Geometry	5.5	proof	—	open
295	Geometry	5.5	proof	—	open
296	Geometry	5.5	proof	—	open
297	Geometry	5.5	proof	—	open
298	Geometry	5.5	proof	—	open
299	Geometry	5.5	proof	—	open
300	Geometry	5.5	proof	—	open
301	Combinatorics	5.5	proof	—	open
302	Geometry	5.5	proof	—	open
303	Geometry	5.5	proof	—	open
304	Algebra	5.5	proof	—	open
305	Geometry	5.5	proof	—	open
306	Combinatorics	5.5	proof	—	open
307	Geometry	5.5	proof	—	open
308	Geometry	5.5	proof	—	open
309	Geometry	5.5	proof	—	open
310	Geometry	5.5	proof	—	open
311	Geometry	5.5	proof	—	open
312	Algebra	5.5	proof	—	open
313	Number theory	5.5	proof	—	open
314	Combinatorics	5.5	proof	—	open
315	Number theory	5.6	proof	—	open
316	Algebra	5.6	proof	—	open
317	Combinatorics	5.6	proof	—	open
318	Geometry	5.6	proof	—	open
319	Geometry	5.6	proof	—	open
320	Number theory	5.6	proof	—	open
321	Geometry	5.6	proof	—	open
322	Combinatorics	5.6	proof	—	open
323	Combinatorics	5.6	proof	—	open
324	Geometry	5.6	proof	—	open
325	Combinatorics	5.6	proof	—	open
326	Combinatorics	5.6	proof	—	open
327	Combinatorics	5.7	proof	—	open
328	Algebra	5.7	proof	—	open
329	Algebra	5.7	proof	—	open
330	Combinatorics	5.7	proof	—	open
331	Combinatorics	5.7	proof	—	open
332	Combinatorics	5.7	proof	—	open
333	Algebra	5.7	proof	—	open
334	Geometry	5.7	proof	—	open
335	Geometry	5.7	proof	—	open
336	Combinatorics	5.7	proof	—	open
337	Geometry	5.7	proof	—	open
338	Algebra	5.7	proof	—	open
339	Geometry	5.7	proof	—	open
340	Combinatorics	5.7	proof	—	open
341	Combinatorics	5.7	proof	—	open
342	Combinatorics	5.7	proof	—	open
343	Combinatorics	5.7	proof	—	open
344	Combinatorics	5.7	proof	—	open
345	Combinatorics	5.7	proof	—	open
346	Combinatorics	5.7	proof	—	open
347	Geometry	5.7	proof	—	open
348	Algebra	5.8	proof	—	open
349	Combinatorics	5.8	proof	—	open
350	Algebra	5.8	proof	—	open
351	Combinatorics	5.8	proof	—	open
352	Number theory	5.8	proof	—	open
353	Geometry	5.8	proof	—	open
354	Combinatorics	5.8	proof	—	open
355	Geometry	5.8	proof	—	open
356	Combinatorics	5.8	proof	—	open
357	Combinatorics	5.8	proof	—	open
358	Combinatorics	5.8	proof	—	open
359	Algebra	5.8	proof	—	open
360	Combinatorics	5.8	proof	—	open
361	Algebra	5.9	proof	—	open
362	Number theory	5.9	proof	—	open
363	Combinatorics	5.9	proof	—	open
364	Combinatorics	5.9	proof	—	open
365	Number theory	5.9	proof	—	open
366	Combinatorics	5.9	proof	—	open
367	Algebra	6.0	proof	—	open
368	Algebra	6.0	proof	—	open
369	Geometry	6.0	proof	—	open
370	Combinatorics	6.0	proof	—	open
371	Combinatorics	6.0	proof	—	open
372	Combinatorics	6.0	proof	—	open
373	Geometry	6.0	proof	—	open
374	Combinatorics	6.0	proof	—	open
375	Combinatorics	6.0	proof	—	open
376	Geometry	6.0	proof	—	open
377	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.