IMO 1979 Shortlist
IMO 1979 Shortlist — 26 problems. 26 problems.
IMO 1979 Shortlist
26 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BEL | Prove that in the Euclidean plane every regular polygon having |
| 2 | BEL | From a bag containing 5 pairs of socks, each pair a different |
| 3 | BUL | Find all polynomials f(x) with real coefficients for which |
| 4 | BUL | A pentagonal prism A1A2 . . . A5B1B2 . . . B5 is given. The |
| 5 | CZS | Let n \geq2 be an integer. Find the maximal cardinality of a set |
| 6 | CZS | Find the real values of p for which the equation |
| 7 | FRG | Given that 1 −1 |
| 8 | FRG | For all rational x satisfying 0 \leqx < 1, f is defined by |
| 9 | FRG | Let S and F be two opposite vertices of a regular octagon. |
| 10 | FIN | Show that for any vectors a, b in Euclidean space, |
| 11 | GDR | Given real numbers x1, x2, . . . , xn (n \geq2), with xi \geq1/n |
| 12 | GDR | Let R be a set of exactly 6 elements. A set F of subsets of R |
| 13 | GRE | Show that 20 |
| 14 | GRE | Find all bases of logarithms in which a real positive number |
| 15 | ISR | The nonnegative real numbers x1, x2, x3, x4, x5, a satisfy the |
| 16 | ISR | Let K denote the set {a, b, c, d, e}. F is a collection of 16 different |
| 17 | NET | Inside an equilateral triangle ABC one constructs points P, |
| 18 | POL | Let m positive integers a1, . . . , am be given. Prove that there |
| 19 | ROM | Consider the sequences (an), (bn) defined by |
| 20 | SWE | Given the integer n > 1 and the real number a > 0 determine |
| 21 | USS | Let N be the number of integral solutions of the equation |
| 22 | USS | There are two circles in the plane. Let a point A be one |
| 23 | USA | Find all natural numbers n for which 28 + 211 + 2n is a perfect |
| 24 | USA | A circle O with center O on base BC of an isosceles triangle |
| 25 | USA | Given a point P in a given plane \pi and also a given point |
| 26 | YUG | Prove that the functional equations |