International Mathematical Olympiad 2018 (Cluj-Napoca, Romania) Scores

At the 2018 IMO held in Cluj-Napoca, Romania, 594 contestants from 107 countries competed. 48 gold medals were awarded to those scoring at least 31; 98 silver medals were awarded to those scoring from 25 to 30; and 143 bronze medals were awarded to those scoring from 16 to 24.

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 15.453, with a standard deviation of 10.530. The following table shows how many contestants attained each possible score.

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

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	4.934	2.946	0.278	3.961	2.695	0.638
Standard deviation	2.924	2.754	1.125	3.015	2.952	1.457

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		0.565	0.174	0.464	0.436	0.249
2	0.565		0.303	0.588	0.607	0.383
3	0.174	0.303		0.219	0.307	0.334
4	0.464	0.588	0.219		0.570	0.337
5	0.436	0.607	0.307	0.570		0.369
6	0.249	0.383	0.334	0.337	0.369

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	96	54	24	15	10	7	7	381
Question 2	158	85	87	66	18	16	7	157
Question 3	548	7	9	14	4	1	0	11
Question 4	148	13	106	18	18	15	5	271
Question 5	175	184	31	7	6	8	11	172
Question 6	419	108	26	11	5	2	5	18
Total	1544	451	283	131	61	49	35	1010

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Contact: Joseph Myers (jsm@polyomino.org.uk)
Last updated: 12 July 2018

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

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

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