How many total squares are there in the figure?
Solve this by combination theory and step by step.
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Given : 4 x 4 Square
To Find : total squares
Solution:
Single Square 1 x 1 = 16
Square 2 x 2 = 9
Square 3 x 3 = 4
Square 4 x 4 = 1
Total Square = 16 + 9 + 4 + 1 = 30
Rule for n x n
Number of Squares = 1² + 2² + _______ + n²
= n(n + 1)(2n + 1)/6
Substitute n = 4 here
= 4 ( 4 + 1) ( 2(4) + 1) /6
= 4 ( 5) ( 9) / 6
= 180/6
= 30
Hence total 30 Squares are there
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