Friday, December 18, 2015

How many squares are there?

How many squares are there?

Usually, we get some puzzle like this. I would like to share trick that can solve this kind of puzzle so easily.
In perfect 4*4 square, to find out the number of squares,
4^2=16
3^2=9
2^2=4
1^1=1
Total number of squares would be 16+9+4+1=30.

Same ways, the answer for squares in 7*7 is,
49+36+25+16+9+4+1=140.

This works perfectly fine when there are same number of rows and columns.

But what if, there are different numbers of rows and columns into it.
For Example,

if there is a rectangle, which has 5 rows and 4 columns and still we have to find the total number of square in it. It would not be possible with the above method.

For this, there is a simple trick,

Rows- 5 Column-4

STEP 1) Multiply the number of rows into number of column
In this case 5*4 = 20
STEP 2) Reduce 1 from number of rows and column
In this case 4*3 = 12
STEP 3) Follow STEP 2 until either of row or column count comes to 1.
In this case 3*2 = 6, 2*1 =2

As we see above the column count has come to 1 so reducing it to zero wont make any sense. 

Total = 20 + 12 + 6 + 2 = 40

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