HMMT 2010 U20

Find the volume of the set of points $(x, y, z)$ satisfying

$\begin{aligned} x, y, z & \geq 0 \\ x+y & \leq 1 \\ y+z & \leq 1 \\ z+x & \leq 1 \end{aligned}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{1}{4}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.