14th International
Mathematical Olympiad:
1972

About 15,000 pupils in schools participated in the 1972 National Mathematics Contest, and 92 of these were invited to take part in the British Mathematical Olympiad. Invitations went to high-scorers on NMC; also to some lower scoring girls, and to a few pupils strongly recommended by their teachers.

Good performances on the NMC and results in BMO are announced in “Science Teacher”. Its editorial director is Maurice Goldsmith, who is chairman of the Awards Committee of the Mathematical Association, which sponsors the British entry to the International Mathematical Olympiad.

Following the British Mathematical Olympiad there was this year a Further International Selection Test. The FIST paper contained four questions, the best three to count, to be done in three hours, the questions being much more like IMO questions. The BMO attaches importance to speed and covers topics in English A-level syllabus such as calculus, mechanics, probability, which do not appear in IMO papers.

As a result the following team was finally chosen: D. J. Allwright (Rugby School), M. Carstairs (George Watson’s College, Edinburgh), D. J. Goto (St Paul’s School), A. J. James (Sherborne School), I. Holyer (St Benedict’s School, Ealing), D. J. Jackson (Perse School), P. Jackson (Royal Grammar School, Newcastle), J. E. Macey (Nottingham High School).

Mr. R. C. Lyness, head of the Bristol Delegation, went to Warsaw on 6 July, two days before the deputy-head, Mrs. Margaret Brown (Chelsea Centre for Science Education), who travelled with the team.

The Olympiad itself was held in Torun. The Jury consisted of the 14 heads of delegations, who met under the Chairmanship of Professor Balcernik, professor of mathematics at the University of Torun, and all meetings were attended by three or four Polish university mathematicians who had been responsible for selecting about 15 problems from those submitted some weeks before by participating countries. Three of the British problems were considered, and two finally selected. The proceedings were conducted almost entirely in English, which nearly all present spoke well.

None of the six questions finally selected was of a type to be found in British examinations, except possibly in the “Further Mathematics” papers set for entrance scholarships in Oxford and Cambridge. (These latter are three-hour papers containing over a dozen questions and often accompanied by hints). The Olympiad questions tested knowledge of the box-principle, plane geometry, number theory, inequalities, functional equations, and solid geometry. Ideas, rather than technique, were favoured.

The procedure followed was as in previous Olympiads. When the teams arrived they were taken off to student hostels, and each team was looked after by a young Polish graduate. The heads of delegation and their deputies, who joined the later jury deliberations, were kept incommunicado from their teams until after the questions were done. Before that we saw our team only from the platform at the opening ceremony.

The leader and deputy-leader marked the scripts of their own team. The marks for each question were co-ordinated by two Polish mathematicians who visited the marking room of each country, discussed and finally agreed the mark for each competitor’s answer. The marks of the Polish competitors were co-ordinated by the delegates from the country which had proposed the question.

Co-ordinators varied in severity, but provided they were consistent this was fair enough. Disputes between co-ordinators and leaders were referred to the jury, and I had to adjudicate the only four disputes which were all concerned with question 3.

Some members of our team did not present their solutions well. If an argument was not properly presented it lost marks. Some of our boys have, perhaps an unfortunate belief that a solution is good if it is short, and that the marker should supply the missing steps. Although special prizes are given for elegance (only one, to a Romanian, this year), a correct but lengthy solution did not lose marks. Many marks, however, were lost for incomplete solutions, and for wrong arguments which were left in a solution even if a sound logical chain could be found which was independent of them.

Each country’s total marks per individual and per question, and their grand totals are given in Tables 1 and 2. The Olympiad is intended not to be a competition between countries, but an opportunity for individuals to show their prowess. The prize list is shown in Table 2. Two of the British team, Jackson, D. and Allwright, got second prizes, and four got third prizes.

The team put up a respectable performance, and came fifth in the order and, as usual, first among the Western participants, leading Austria Sweden and the Netherlands. France could not take part because of a clash of dates with Baccalauréat. Belgium and Italy have participated in the past. West Germany sent an observer, and may participate in future. They have started a national competition, but they think their present standards not high enough for these ingenious problems set within the confines of the IMO “syllabus”.

There was great friendliness and frankness in discussions, formal as well as informal, and it appears there would be jubilation if Great Britain were to offer to be the host country. Next year, the likelihood is that Bulgaria will be host, but this awaits official confirmation.

Sweden and the Netherlands are helped by grants from their Governments. West Germany has obtained considerable help from a kind of Nuffield Foundation for Science which is financed by their motor industry.

Each year the matter of raising money for our participation causes anxiety. The invitations are at Government level, and our Department of Education and Science has accepted invitations on the understanding that the Mathematical Association sponsors the educational side, selects the team and leaders, submits problems, and raises money from private sources. The Guinness Company, which pays for the organising and prizes for the National Mathematical Contest and the British Mathematical. Olympiad, has through Maurice Goldsmith’s office made all administrative arrangements eg travel, passport-visas.

There is usually a credit balance available from money received for the NMC. This year special contributions were made by the London Mathematical Society and from the MEI committee of the Mathematical Association.

What the Guinness Company contributes is variable. One previous year the company paid for all IMO expenses. As a result of these competitions, “Science Teacher” gets some material, such as problems, solutions, lists of prize winners, and accounts of IMO visits, but the Guinness Company must get very little publicity and acts truly with enlightened dis-interest in the cause of stimulating mathematical education in this country.

This report is concerned with the IMO; the undoubted national worth of the NMC and BMO are not under discussion. The IMO is more costly. It is of direct value to those participating. Like participation in the Olympic Games, it is an individual élitist thing and is concerned with high standards; it presents a goal for young able mathematicians.

(The Awards Committee of the Mathematical Association has submitted the above account.)

Report reproduced from Science Teacher volume 16 number 1 (October 1972) pages 3 and 4.

Table 1

Marks by Questions

Table 2

All Teams — Individual Marks

Prizes: 1st, 40; 2nd, 39-30; 3rd, 29-19

Tables reproduced from Science Teacher volume 16 number 1 (October 1972) page 6.

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