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 .                                   

                                                                      .sq 1

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
3 4
 3  3 4

 

  5  
   5  
  6  
   6  

 

       
7 8
 7  7  8
       

 

       
  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  
       
  2  2  2
   2  2
   2  2
       

 

       
3  3  
 3  3  
 3  3  

 

       
  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 .