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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

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