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Building from bricks

Source: St Petersburg Olympiad 2011, Grade 11, P3

September 15, 2017
combinatorics

Problem Statement

Can we build parallelepiped 6×7×76 \times 7 \times 7 from 1×1×21 \times 1 \times 2 bricks, such that we have same amount bricks of one of 33 directions ?
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