International Mathematical Olympiad 1991 (Sigtuna, Sweden) Scores

At the 1991 IMO held in Sigtuna, Sweden, 312 contestants from 55 countries competed. 20 gold medals were awarded to those scoring at least 39; 51 silver medals were awarded to those scoring from 31 to 38; and 84 bronze medals were awarded to those scoring from 19 to 30.

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 9 contestants attained). The mean individual score was 19.314, with a standard deviation of 12.368. The following table shows how many contestants attained each possible score.

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

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	3.798	4.221	2.558	3.128	3.801	1.808
Standard deviation	3.087	2.770	2.069	3.028	3.061	2.597

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		0.532	0.344	0.385	0.497	0.364
2	0.532		0.547	0.588	0.530	0.487
3	0.344	0.547		0.477	0.376	0.521
4	0.385	0.588	0.477		0.360	0.504
5	0.497	0.530	0.376	0.360		0.454
6	0.364	0.487	0.521	0.504	0.454

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	93	27	10	3	34	8	6	131
Question 2	47	34	21	27	31	6	16	130
Question 3	90	14	16	111	37	16	5	23
Question 4	112	34	15	18	10	15	13	95
Question 5	77	42	18	14	14	6	7	134
Question 6	172	29	27	16	10	5	3	50
Total	591	180	107	189	136	56	50	563

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

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

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

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