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It is very important to save time, when you have to solve multiple questions in a minute.

That is why i make these algorithms to save time while giving exam.

I will show you, how can you make one.

If you have any questions, please comment below. I will reply ASAP.

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Step 1: Make One Square and See What Is the Answer

1 x 1 square

Answer : obviously answer is one.

Step 2: How Many Squares in 2 X 2 Square

2 x 2 Square

Answer : 4 small squares + 1 big square

= 5 squares

Step 3: Same Thing for 3 X 3 Squares and 4 X 4 Squares

3 x 3 Square

Answer : 9 smallest squares + 4 medium size squares + 1 big square

= 14 squares

4 x 4 Square

Answer : 16 smallest squares + 9 medium size squares + 4 big square + 1 giant square

= 30 squares

Step 4: Finally, How Can You Make an Equation

Search for clues in previous steps:

3 x 3 Square
Answer : 9 smallest squares + 4 medium size squares + 1 big square = 14 squares

4 x 4 Square

Answer : 16 smallest squares + 9 medium size squares + 4 big square + 1 giant square = 30 squares

Answer is 30 squares,

Which is 16 (smallest squares in 4 x 4) + 14 (Total squares in 3 x 3)

In 3 x 3 square and 4 x 4 square, there is one similarity,
9 squares + 4 squares + 1 square

Where , 9 squares = 3 multiplied by 3

4 squares = 2 multiplied by 2

1 square = 1 multiplied by 1

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Calculation

You only add smallest number of squares to previous calculation

list all the answers

1x1 Square : (1*1) = 1

2x2 Square : (1*1) + (2*2) = 1+4 = 5

3x3 Square : (1*1) + (2*2) + (3*3) = 1+4+9 = 14

4x4 Square : (1*1) + (2*2) + (3*3) + (4*4) = 1+4+9+16 = 30

5x5 Square : (1*1) + (2*2) + (3*3) + (4*4) + (5*5) = 1+4+9+16+25 = 55

So add up square of one through number of rows as shown above.

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This is how you make equations (see the attached image). If you have any questions, please comment below. I will reply ASAP.

<p>Very Interesting Instructable.</p>
would this be the same logic for triangle based...where you would cube it vs squaring in your example?
<p>x is number of rows.</p><p>When x is an even number, No. of Triangles = 0.125 x(x+2)(2x+1)</p><div>When x is an odd number, No. of Triangles = 0.125 [x(x+2)(2x+1) -1]</div>
<p>I mean this triangles</p>
<p>Little Complex. But I will make instructable for it. </p>
sorry I meant the number of triangles in a overall triangle shape just as your counting squares was in an overall square shape. thanks.
<p>Answer</p>

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