IMO 1974 Shortlist
IMO 1974 Shortlist — 12 problems. 12 problems.
IMO 1974 Shortlist
12 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | — | I 1 (USA 4)IMO1 Alice, Betty, and Carol took the same series of exam- |
| 2 | — | I 2 (POL 1) Prove that the squares with sides 1/1, 1/2, 1/3, . . . may be |
| 3 | — | I 3 (SWE 3)IMO6 Let P(x) be a polynomial with integer coefficients. If |
| 4 | — | I 4 (USS 4) The sum of the squares of five real numbers a1, a2, a3, a4, a5 |
| 5 | — | I 5 (GBR 3) Let Ar, Br, Cr be points on the circumference of a given |
| 6 | — | I 6 (ROM 4)IMO3 Does there exist a natural number n for which the |
| 7 | — | II 1 (POL 2) Let ai, bi be coprime positive integers for i = 1, 2, . . . , k, |
| 8 | — | II 2 (NET 3)IMO5 If a, b, c, d are arbitrary positive real numbers, find all |
| 9 | — | II 3 (CUB 3) Let x, y, z be real numbers each of whose absolute value |
| 10 | — | II 4 (FIN 3)IMO2 Let \triangleABC be a triangle. Prove that there exists a |
| 11 | — | II 5 (BUL 1)IMO4 Consider a partition of an 8 \times 8 chessboard into p |
| 12 | — | II 6 (USS 1) In a certain language words are formed using an alphabet |