International Mathematical Olympiad 2021 (St Petersburg (virtual), Russia) Scores

At the 2021 IMO held in St Petersburg (virtual), Russia, 619 contestants from 107 countries competed. 52 gold medals were awarded to those scoring at least 24; 103 silver medals were awarded to those scoring from 19 to 23; and 148 bronze medals were awarded to those scoring from 12 to 18.

Further statistics are shown below. Detailed tables of results by country or contestant are available:

Total scores of each country, in descending order of total score (the IMO is an individual competition, so country orderings are unofficial only).
Total scores of each country, in alphabetical order.
Individual scores, in descending order of score.
Individual scores, in order of contestant code.

The maximum individual score possible was 42 (which only one contestant attained). The mean individual score was 11.590, with a standard deviation of 9.241. The following table shows how many contestants attained each possible score.

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	0
36	7
35	3
34	0
33	2
32	2
31	3
30	4
29	8
28	9
27	6
26	1
25	0
24	5
23	10
22	42
21	37
20	9
19	5
18	8
17	3
16	13
15	38
14	50
13	22
12	14
11	15
10	13
9	16
8	24
7	43
6	11
5	13
4	20
3	11
2	29
1	34
0	87

The following table shows the maximum attainable score, mean score and standard deviation of scores for each individual question.

Question number	1	2	3	4	5	6
Maximum score	7	7	7	7	7	7
Mean score	4.393	0.375	0.372	3.817	2.152	0.481
Standard deviation	2.913	1.251	1.137	3.296	3.142	1.697

The following table shows the correlation coefficients between the scores on each pair of questions. To make sense of these figures you will probably wish to look at the problems themselves (from Mathlinks) to see which are on similar or different topics.

	1	2	3	4	5	6
1		0.231	0.240	0.537	0.458	0.215
2	0.231		0.202	0.221	0.325	0.330
3	0.240	0.202		0.290	0.240	0.377
4	0.537	0.221	0.290		0.382	0.229
5	0.458	0.325	0.240	0.382		0.391
6	0.215	0.330	0.377	0.229	0.391

The following table shows the distribution of scores on each individual question with the total number of each score on any question.

	Score 0	Score 1	Score 2	Score 3	Score 4	Score 5	Score 6	Score 7
Question 1	131	36	41	10	41	39	35	286
Question 2	522	61	12	2	3	1	2	16
Question 3	488	110	4	1	1	0	0	15
Question 4	218	33	39	2	12	1	5	309
Question 5	404	12	13	4	2	5	4	175
Question 6	562	12	2	3	1	2	0	37
Total	2325	264	111	22	60	48	46	838

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Contact: Joseph Myers (jsm@polyomino.org.uk)
Last updated: 23 July 2021

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	0
36	7
35	3
34	0
33	2
32	2
31	3
30	4
29	8
28	9
27	6
26	1
25	0
24	5
23	10
22	42
21	37
20	9
19	5
18	8
17	3
16	13
15	38
14	50
13	22
12	14
11	15
10	13
9	16
8	24
7	43
6	11
5	13
4	20
3	11
2	29
1	34
0	87

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	0
36	7
35	3
34	0
33	2
32	2
31	3
30	4
29	8
28	9
27	6
26	1
25	0
24	5
23	10
22	42
21	37
20	9
19	5
18	8
17	3
16	13
15	38
14	50
13	22
12	14
11	15
10	13
9	16
8	24
7	43
6	11
5	13
4	20
3	11
2	29
1	34
0	87

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	0
36	7
35	3
34	0
33	2
32	2
31	3
30	4
29	8
28	9
27	6
26	1
25	0
24	5
23	10
22	42
21	37
20	9
19	5
18	8
17	3
16	13
15	38
14	50
13	22
12	14
11	15
10	13
9	16
8	24
7	43
6	11
5	13
4	20
3	11
2	29
1	34
0	87