Question 3
An empty $2020\times2020\times2020$ cube has a unit-square grid on each face. A beam is a $1\times1\times2020$ prism. Its two unit faces must occupy grid cells on opposite cube faces; beam interiors must be disjoint; and the interior of each of its four long faces must touch a cube face or the interior of a face of another beam. Find the smallest positive possible number of beams.
Proposed by Alex Zhai. Source: Evan Chen’s third-party solution notes.
Source video link: https://youtu.be/r7j0oRtpErA?t=2440
Proposed by Alex Zhai. Source: Evan Chen’s third-party solution notes.
Source video link: https://youtu.be/r7j0oRtpErA?t=2440