KURSCHAK 1961 Problem 2

$x, y, z$ are positive reals less than $1$ . Show that at least one of $(1 - x)y$ , $(1 - y)z$ and $(1 - z)x$ does not exceed $\frac14$ .

Dataset text AI-MO AoPS. 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.