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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
avatar+122 
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Well, let's take a deeper look.

 

It's in the 5×5 square.

 

it's in all 4 of the 4×4 squares.

 

it's in all 9 of the 3×3 squares.

 

It's in 4 of the 2×2 squares.

 

It's in 1 of the 1×1 squares.

 

That would leave us with a total of 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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