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Mathematics in Education and Industry (MEI)

MEI is committed to improving mathematics education and promotes teaching and learning through different strands of activity. We support teachers through a range of professional development opportunities, including our annual conference. Innovative resources are continually being developed to extend and enrich your knowledge of mathematics, whether teacher, student, undergraduate or member of the workforce.

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Maths Item of the Month

November 2020
Fault-free tilings

A fault-free tiling is an arrangment of tiles in an m×n grid such that there are no vertical or horizontal lines that can be placed on the grid without crossing one of the tiles.

fault-free tilings

In the image above a 6×4 and a 6×8 grid have been tiled with 2×1 dominoes. The 6×4 tiling has 2 vertical fault lines and is therefore not fault free. The 6×8 tiling is fault-free.

Is it possible, using 2×1 dominoes, to find fault-free tilings of:

  • a 6×5 grid
  • a 6×6 grid
  • a 6×7 grid

Maths item of the month archive

A list of Maths Items of the Month categorised by GCSE/A level topics can be seen at: Maths Items of the Month Curriculum mapping.