International Mathematical Olympiad 2009 (Bremen, Germany) Scores

At the 2009 IMO held in Bremen, Germany, 565 contestants from 104 countries competed. 49 gold medals were awarded to those scoring at least 32; 98 silver medals were awarded to those scoring from 24 to 31; and 135 bronze medals were awarded to those scoring from 14 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 2 contestants attained). The mean individual score was 15.090, with a standard deviation of 10.797. The following table shows how many contestants attained each possible score.

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

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	4.804	3.710	1.019	2.915	2.474	0.168
Standard deviation	2.858	2.903	2.051	2.791	2.982	0.851

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		0.488	0.349	0.417	0.528	0.148
2	0.488		0.445	0.577	0.571	0.161
3	0.349	0.445		0.400	0.568	0.350
4	0.417	0.577	0.400		0.557	0.233
5	0.528	0.571	0.568	0.557		0.265
6	0.148	0.161	0.350	0.233	0.265

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	83	56	28	20	17	16	21	324
Question 2	101	106	43	51	16	15	19	214
Question 3	357	127	16	5	2	5	2	51
Question 4	188	79	37	23	17	69	52	100
Question 5	270	42	50	33	6	4	7	153
Question 6	540	2	1	10	6	2	1	3
Total	1539	412	175	142	64	111	102	845

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

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

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

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