## Reasoning – Counting numbers – Part – I.

Here in this blog we are discussing about Reasoning – Counting numbers – Part – I. Some of the illustrations are :

1.How many squares are there in a square of 4 x 4 cm. Find the count using the reasoning method .

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# SOLUTION :

From the given question we derive a square of 4 x 4 cm .

So there are many possibilities of having squares of measurements from 1 cm up to 4 cm .

On constructing those squares in this basis we arrive at the total of 30 squares .

Following the reasoning trick behind counting the number of squares we can get the answer for this tricky question .

There are 16 squares of 1 x 1 cm ,9 squares of 2 x 2 cm , 4  squares of 3 x 3 cm and  1 square of 4 x 4 cm in it .

Totally there are  16 + 9  + 4  + 1  =  30 squares in it.

From the given diagram we deduce a square with 16 boxes

### The 1 x 1 cm  squares are from 1 to  16.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

### Again from the diagram we get the squares of sizes 2 x 2 cm are from 1 to 9.

 1 1 2 2 1 1 2 2 3 3 4 4 3 3 4 4

 5 5 5 5 6 6 6 6

 7 7 8 8 7 7 8 8

 9 9 9 9

### Finally the possibility of having the  3 x 3 cm squares are from 1 to 4

 1 1 1 1 1 1 1 1 1
 2 2 2 2 2 2 2 2 2

 3 3 3 3 3 3 3 3 3
 4 4 4 4 4 4 4 4 4

### Hence there can exist  4 x 4 cm square is only one.

 1

So from the above reasoning tricky question we at most found the number of squares by counting it from the given diagram .