IMO 1977 Shortlist
IMO 1977 Shortlist — 16 problems. 16 problems.
IMO 1977 Shortlist
16 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BUL | Let f : N \toN be a function that satisfies the inequality |
| 2 | CZS | A lattice point in the plane is a point both of whose coordinates |
| 3 | FRG | Let a and b be natural numbers and let q and r be the |
| 4 | FRG | Describe all closed bounded figures \Phi in the plane any two |
| 5 | FRG | There are 2n words of length n over the alphabet {0, 1}. Prove |
| 6 | GDR | Let n be a positive integer. How many integer solutions |
| 7 | GBR | Let a, b, A, B be given constant real numbers and |
| 8 | GBR | Let S be a convex quadrilateral ABCD and O a point inside |
| 9 | HUN | For which positive integers n do there exist two polynomials f |
| 10 | NET | Let n be an integer greater than 2. Define V = {1 + kn | |
| 11 | NET | Let n be an integer greater than 1. Define |
| 12 | NET | On the sides of a square ABCD one constructs inwardly |
| 13 | POL | Let B be a set of k sequences each having n terms equal to 1 or |
| 14 | — | (FIN 2‘) Let E be a finite set of points such that E is not contained in |
| 15 | VIE | The length of a finite sequence is defined as the number of |
| 16 | VIE | Let E be a set of n points in the plane (n \geq3) whose co- |