DIY Challenge 4: Tiling with dominoes
Tiling with Dominos
The following is a 5×5 square with one position blocked. Will we be able to cover this with Dominos? Why?
What is the condition needed to cover any square grid with dominos?
What students worked out5
Student 4
1).The grid dimensions should be multiples of 2
Student 13
Sir it is not possible. In a square grid, if we colour the tiles black and white (like a chess board), the number of white and black tiles are unequal. As one domino covers only one white and one black tile we will have two tiles of the same colour left. However if we place a blocking square in the middle we can easily tile a 5×5 grid using dominoes.
Student 3
NOT POSSIBLE SIR
Student 3
BLOCKING WITH THESE SQUARES ONLY IS POSSIBLE
Student 2
12 white squares and 12 black squares or white squares==black squares