RU-ALLRUSSIAN 1990 Problem 23
A game is played in three moves. The first player picks any real number, then the second player makes it the coefficient of a cubic, except that the coefficient of is already fixed at 1. Can the first player make his choices so that the final cubic has three distinct integer roots?
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.