MathDB

unrestricted supply of bricks 1 x 1 x 3, 3 cubes 1x1x1, box m x n x k

Source: Tournament of Towns, Junior O-Level , Fall 2019 p5

April 19, 2020

combinatoricsTilingtiles

Problem Statement

Basil has an unrestricted supply of straight bricks

1 \times 1 \times 3

and Γ-shape bricks made of three cubes

1\times 1\times 1

. Basil filled a whole box

m \times n \times k

with these bricks, where

m, n

and

k

are integers greater than

1

. Prove that it was sufficient to use only Γ-shape bricks.
(Mikhail Evdokimov)