International Mathematical Olympiad 2013 (Santa Marta, Colombia) Scores

At the 2013 IMO held in Santa Marta, Colombia, 527 contestants from 97 countries competed. 45 gold medals were awarded to those scoring at least 31; 92 silver medals were awarded to those scoring from 24 to 30; and 141 bronze medals were awarded to those scoring from 15 to 23.

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 no‐one attained). The mean individual score was 15.609, with a standard deviation of 10.356. The following table shows how many contestants attained each possible score.

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

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	4.108	2.526	0.786	5.442	2.452	0.296
Standard deviation	3.170	2.836	2.004	2.733	2.985	1.165

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		0.501	0.277	0.429	0.541	0.229
2	0.501		0.158	0.302	0.532	0.328
3	0.277	0.158		0.218	0.413	0.208
4	0.429	0.302	0.218		0.388	0.141
5	0.541	0.532	0.413	0.388		0.336
6	0.229	0.328	0.208	0.141	0.336

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	118	96	9	6	14	3	5	276
Question 2	229	32	65	33	22	12	16	118
Question 3	438	10	15	16	0	3	4	41
Question 4	82	16	14	14	2	5	9	385
Question 5	235	84	33	11	0	10	19	135
Question 6	481	15	6	6	2	6	4	7
Total	1583	253	142	86	40	39	57	962

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Contact: Joseph Myers (jsm@polyomino.org.uk)
Last updated: 5 January 2016

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

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

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