MathDB
Packing bricks into a box, but exactly how many?

Source: Baltic Way 2020, Problem 7

November 14, 2020
combinatoricscombinatorics proposed

Problem Statement

A mason has bricks with dimensions 2×5×82\times5\times8 and other bricks with dimensions 2×3×72\times3\times7. She also has a box with dimensions 10×11×1410\times11\times14. The bricks and the box are all rectangular parallelepipeds. The mason wants to pack bricks into the box filling its entire volume and with no bricks sticking out. Find all possible values of the total number of bricks that she can pack.
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