International Mathematical Olympiad 1987 (Havana, Cuba) Scores

At the 1987 IMO held in Havana, Cuba, 237 contestants from 42 countries competed. 22 gold medals were awarded to those scoring at least 42; 42 silver medals were awarded to those scoring from 32 to 41; and 56 bronze medals were awarded to those scoring from 18 to 31.

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 22 contestants attained). The mean individual score was 19.928, with a standard deviation of 13.719. The following table shows how many contestants attained each possible score.

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

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	3.447	4.776	2.105	3.527	4.249	1.823
Standard deviation	3.152	2.978	2.961	3.101	3.088	2.607

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		0.476	0.593	0.632	0.608	0.523
2	0.476		0.394	0.388	0.450	0.355
3	0.593	0.394		0.586	0.480	0.595
4	0.632	0.388	0.586		0.496	0.545
5	0.608	0.450	0.480	0.496		0.431
6	0.523	0.355	0.595	0.545	0.431

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	74	32	16	7	3	7	1	97
Question 2	51	9	7	12	7	4	4	143
Question 3	125	41	5	1	0	2	6	57
Question 4	75	20	21	9	2	12	7	91
Question 5	59	21	8	5	9	10	6	119
Question 6	127	32	12	12	8	5	4	37
Total	511	155	69	46	29	40	28	544

Return to IMO Scores home page
Return to my mathematics page
Return to my home page

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

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

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

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