A storage depot is a pyramid with height 30 and a square base with side length 40. Determine how many cubical 3 × 3 × 3 boxes can be stored in this depot if the boxes are always packed so that each of their edges is parallel to either an edge of the base or the altitude of the pyramid.

Source: Purple Comet Math Meet

The answer is 471.

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Link: https://purplecomet.org/views/data/2020MSSolutions.pdf