Introduction: How to Create Algorithm to Calculate Squares Faster in IQ Exams and Challenges

Picture of How to Create Algorithm to Calculate Squares Faster in IQ Exams and Challenges

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

Picture of 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

Picture of 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

Picture of 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

Picture of 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.

Comments

Jonathanrjpereira (author)2016-05-10

Very Interesting Instructable.

rajmchavda (author)2016-04-28

would this be the same logic for triangle based...where you would cube it vs squaring in your example?

hjajadiya (author)rajmchavda2016-05-05

x is number of rows.

When x is an even number, No. of Triangles = 0.125 x(x+2)(2x+1)

When x is an odd number, No. of Triangles = 0.125 [x(x+2)(2x+1) -1]
hjajadiya made it! (author)hjajadiya2016-05-05

I mean this triangles

hjajadiya (author)rajmchavda2016-04-28

Little Complex. But I will make instructable for it.

rajmchavda (author)hjajadiya2016-05-05

sorry I meant the number of triangles in a overall triangle shape just as your counting squares was in an overall square shape. thanks.

hjajadiya made it! (author)2016-04-29

Answer

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