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# counting question

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The 5*5 grid shown contains a collection of squares with sizes from 1*1 to 5*5. How many of these squares contain the black square?

Dec 29, 2020

#1
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Well, let's take a deeper look.

It's in the $$5\times5$$ square.

it's in all $$4$$ of the $$4\times4$$ squares.

it's in all $$9$$ of the $$3\times3$$ squares.

It's in $$4$$ of the $$2\times2$$ squares.

It's in $$1$$ of the $$1\times1$$ squares.

That would leave us with a total of $$\boxed{19}$$ squares.

Dec 29, 2020
#2
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it's in all  9 of the 3 x 3   squares.        How is that !?   I see  only 4 ......

Guest Dec 29, 2020
#3
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guest, i think you're right, there is only 4 3 by 3 squares that include that black square. There are 9 squares in total, and the answerer might have been confused.

So the total number of squares that include that black square is 1 + 4 +4 +4 + 1 = 14 squares.

textot  Dec 29, 2020