International Mathematical Olympiad 2005 (Merida, Mexico) Scores

At the 2005 IMO held in Merida, Mexico, 513 contestants from 91 countries competed. 42 gold medals were awarded to those scoring at least 35; 79 silver medals were awarded to those scoring from 23 to 34; and 128 bronze medals were awarded to those scoring from 12 to 22.

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 16 contestants attained). The mean individual score was 13.850, with a standard deviation of 11.826. The following table shows how many contestants attained each possible score.

Score	Number of contestants
42	16
41	2
40	1
39	1
38	2
37	6
36	6
35	8
34	3
33	1
32	6
31	4
30	8
29	7
28	17
27	4
26	7
25	8
24	6
23	8
22	9
21	8
20	5
19	12
18	19
17	16
16	16
15	18
14	13
13	5
12	6
11	12
10	16
9	19
8	26
7	6
6	13
5	15
4	12
3	28
2	49
1	41
0	28

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	2.614	3.051	0.912	3.758	2.170	1.345
Standard deviation	2.941	2.975	2.263	3.124	2.966	2.297

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		0.438	0.325	0.408	0.457	0.374
2	0.438		0.339	0.472	0.428	0.564
3	0.325	0.339		0.322	0.449	0.409
4	0.408	0.472	0.322		0.377	0.409
5	0.457	0.428	0.449	0.377		0.340
6	0.374	0.564	0.409	0.409	0.340

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	207	59	65	20	5	11	5	141
Question 2	96	202	13	7	11	7	2	175
Question 3	423	23	3	0	0	0	9	55
Question 4	90	145	30	0	0	3	7	238
Question 5	288	36	30	16	4	6	8	125
Question 6	325	39	57	13	15	2	6	56
Total	1429	504	198	56	35	29	37	790

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

Score	Number of contestants
42	16
41	2
40	1
39	1
38	2
37	6
36	6
35	8
34	3
33	1
32	6
31	4
30	8
29	7
28	17
27	4
26	7
25	8
24	6
23	8
22	9
21	8
20	5
19	12
18	19
17	16
16	16
15	18
14	13
13	5
12	6
11	12
10	16
9	19
8	26
7	6
6	13
5	15
4	12
3	28
2	49
1	41
0	28

Score	Number of contestants
42	16
41	2
40	1
39	1
38	2
37	6
36	6
35	8
34	3
33	1
32	6
31	4
30	8
29	7
28	17
27	4
26	7
25	8
24	6
23	8
22	9
21	8
20	5
19	12
18	19
17	16
16	16
15	18
14	13
13	5
12	6
11	12
10	16
9	19
8	26
7	6
6	13
5	15
4	12
3	28
2	49
1	41
0	28

Score	Number of contestants
42	16
41	2
40	1
39	1
38	2
37	6
36	6
35	8
34	3
33	1
32	6
31	4
30	8
29	7
28	17
27	4
26	7
25	8
24	6
23	8
22	9
21	8
20	5
19	12
18	19
17	16
16	16
15	18
14	13
13	5
12	6
11	12
10	16
9	19
8	26
7	6
6	13
5	15
4	12
3	28
2	49
1	41
0	28