14x14 grid
Posted: Wed Apr 26, 2017 6:37 pm
Is it possible to completely completely a $$14$$x$$14$$ grid by T shaped blocks from the diagram such that no blocks overlaps any other block?Explain the answer with logic
Put $1$ and $0$ alternately in that grid. Then in any $T$ shape, $2$ configuration is possible:
#1 three $1$'s and one $0$'s
#2 three $0$'s and one $1$'s
In both configuration, the sum of the numbers in that $T$ is odd. The grid is $14 x 14$. So, we need an odd number of $T$ - tiles. The initial sum is odd then. But if we put $1$ and $0$ alternately, the initial sum must be an even. Contradiction!
#1 three $1$'s and one $0$'s
#2 three $0$'s and one $1$'s
In both configuration, the sum of the numbers in that $T$ is odd. The grid is $14 x 14$. So, we need an odd number of $T$ - tiles. The initial sum is odd then. But if we put $1$ and $0$ alternately, the initial sum must be an even. Contradiction!