RU-SPB 2011 Problem 113

Can we build parallelepiped $6 \times 7 \times 7$ from $1 \times 1 \times 2$ bricks, such that we have same amount bricks of one of $3$ directions ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.