IMO 1971 Shortlist
IMO 1971 Shortlist — 17 problems. 17 problems.
IMO 1971 Shortlist
17 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BUL | Consider a sequence of polynomials P0(x), P1(x), P2(x), . . . , |
| 2 | BUL | Prove that for every natural number m \geq1 there exists a |
| 3 | GDR | Knowing that the system |
| 4 | GBR | We are given two mutually tangent circles in the plane, with |
| 5 | HUN | Let a, b, c, d, e be real numbers. Prove that the expression |
| 6 | HUN | Let n \geq2 be a natural number. Find a way to assign nat- |
| 7 | NET | Given a tetrahedron ABCD whose all faces are acute- |
| 8 | NET | Determine whether there exist distinct real numbers a, b, c, t |
| 9 | POL | Let Tk = k −1 for k = 1, 2, 3, 4 and |
| 10 | POL | Prove that the sequence 2n −3 (n > 1) contains a subse- |
| 11 | POL | The matrix |
| 12 | POL | Two congruent equilateral triangles ABC and A′B′C′ in the |
| 13 | SWE | Consider the n \times n array of nonnegative integers |
| 14 | USS | A broken line A1A2 . . . An is drawn in a 50\times50 square, so that |
| 15 | USS | Natural numbers from 1 to 99 (not necessarily distinct) are |
| 16 | USS | Given a convex polyhedron P1 with 9 vertices A1, . . . , A9, |
| 17 | YUG | Prove the inequality |