IMO 1974 Shortlist

IMO 1974 Shortlist — 12 problems. 12 problems.

12 items

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