#16. Covering a Cube Minus One Vertex

(Back to course page.)

Link to Slides · Link to recording

---

Prompts for discussion:

1. We saw during the discussion two different ways of covering the cube minus the origin with (d) hyperplanes: we can use the hyperplanes \(\left\{x_i=1\right\}, i=1,2, \ldots, d\), or the hyperplanes \(\left\{x_1+x_2+\cdots+x_d=k\right\}, k=1,2, \ldots, d\). Are there other ways? Can all the ways be counted?

2. What happens if you are trying to avoid two points? Note that it now perhaps matters which two!