Shortcut methods to count the number of boxes
Here, you will learn fast methods to count the number of boxes in the given diagram.

Shortcuts to Count Boxes (Squares)

Case-1

If number of small squares in horizontal and vertical directions are same. As in the adjacent figure. Five horizontally and five vertically.
Then Total number of squares (small and big) = sum of squares of all the numbers starting from 1 to maximum value.
So in the present case Total squares = 12+22+32+42+52
Total Squares = 55


Case-2

If number of small squares in horizontal and vertical directions are not same. Then you can compute total squares as given below:
Total squares = (maximum horizontal value) X (maximum vertical value) + (max horizontal value - 1) X (maximum vertical value -1)+(max horizontal value - 2) X (maximum vertical value -2)... this process will continue till you get a zero.
In the present case total squares
= (5 X 3) + (4 X 2) + (3 X 1) +(2 X 0)
So Total Squares = 15+8+3 = 26


Case-3

Clearly observe that in this type of pattern
Total squares = 4 + 1 (outer big black square)
This is called plus-pattern. So, when we have a plus pattern inside a square, Total squares = 5


Case-4

Clearly, In this case, we have four big squares (black,red,green,blue) with plus-patterns.
So Total plus patterns = 4
So Total number of squares = 4 X 5 = 20
because each plus pattern = 5 squares, as discussed in case-3.


Case-5

In this case total number of small black squares in horizontal and vertical directions are equal. and each count is equal to 4. Total black squares = 12+22+32+42 (discussed in case-1)
So total black squares = 1+4+9+16 = 30 --> (1)
Now total red plus-patterns = 4. (case-3)
Total green plus-patterns = 4. (case-3)
Total plus patterns = 4+4 = 8.
Number of squares in 1 plus-patter = 5.
So squares in all plus pattern = 8 X 5 = 40.--> (2)
So total number of squares = 30 + 40 =70. (from 1 and 2)


Case-6

Clearly , In this type of pattern, there is one plus-pattern and one red tilted square.
So, Total number of squares = 5+1 = 6.
So keep this thing in mind that this pattern will have 6 squares.


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