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BdMO Online Forum • View topic - 14x14 grid

14x14 grid

For students of class 6-8 (age 12 to 14)
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14x14 grid

Post Number:#1  Unread postby jayon_2 » 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
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Re: 14x14 grid

Post Number:#2  Unread postby Atonu Roy Chowdhury » Thu Apr 27, 2017 12:12 am

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!
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