International Mathematical Olympiad 1996 (Mumbai (Bombay), India) Scores

At the 1996 IMO held in Mumbai (Bombay), India, 426 contestants from 75 countries competed (counting 2 contestants with scores of ‘– – – – – -’). 35 gold medals were awarded to those scoring at least 28; 66 silver medals were awarded to those scoring from 20 to 27; and 99 bronze medals were awarded to those scoring from 12 to 19.

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 only one contestant attained). The mean individual score was 12.401, with a standard deviation of 9.551. The following table shows how many contestants attained each possible score.

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

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	3.160	2.021	2.387	2.110	0.491	2.232
Standard deviation	2.232	2.732	2.256	2.736	1.151	2.892

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		0.210	0.450	0.370	0.078	0.418
2	0.210		0.411	0.431	0.330	0.237
3	0.450	0.411		0.480	0.245	0.543
4	0.370	0.431	0.480		0.247	0.295
5	0.078	0.330	0.245	0.247		0.186
6	0.418	0.237	0.543	0.295	0.186

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	69	30	98	26	111	17	12	63
Question 2	180	124	10	5	11	6	2	88
Question 3	51	176	73	22	14	19	19	52
Question 4	179	109	11	17	11	7	6	86
Question 5	313	74	18	7	4	4	0	6
Question 6	198	79	16	15	3	6	10	99
Total	990	592	226	92	154	59	49	394

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

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

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

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