Reasoning – Counting numbers – Part – I

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 .           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 .