Basic Calculation-02

1, SQUARES OF NUMBERS MADE OF ONES ONLY

 (i)  11²  =  121         [Since No. of one = 2 = Maximum no.]                                   

(ii)  111²  =  12321       [Since No. of one =3 = Maximum no]                                                

(iii)  1111²  =  1234321  [Since No. of one = 4 = Maximum no]                 

(iv)  11111²  =  123454321  [Since No. of one = 5 = Maximum no]                                

(v)  111111²  =  12345654321  [Since No. of one = 6 = Maximum no]                            

(vi)  1111111²  =  1234567654321  [Since No. of one = 7 = Maximum no]                            

(vii)  11111111²  =  123456787654321  [Since No. of one = 8 = Maximum no]                             

(viii)  111111111²  =  12345678987654321 [Since No. of one = 9 = Maximum no]                            

2. MULTIPLICATION OF TWO NUMBERS MADE OF ONES ONLY

(i)  11 ´ 111  =   1221

(ii)  11 ´ 1111  =   12221

(iii)  11 ´ 11111  =   122221

(iv)  11 ´ 111111  =   1222221              

(v)  11 ´ 1111111  =  12222221                               

(vi)  111 ´ 1111  =  123321  

(vii)  111 ´ 11111  =  1233321  

(viii)  111 ´ 111111  =  12333321  

(ix)  111 ´ 1111111  =  123333321  

(x)  111 ´ 11111111  =  1233333321  

(xi)  1111 ´ 11111  =  12344321                           

(xii)  1111 ´ 111111  = 123444321                           

(xiii)  1111 ´ 1111111  = 1234444321

(xiv)  1111 ´ 11111111  = 12344444321

[Concept: First of all, the no. of ones in the smaller no. is the Maximum No. For example, in “111 ´ 11111”^,  111 is the smaller no. in which no. of ones is 3, so the maximum no, is 3; up to which we have to go from 1.

Second, the difference between the no. of ones is 2 {no. of ones in 111 is 3 and the no. of ones in 11111 is 5; and the difference between 5 and 3 is 2}.

Third, the maximum no. is written as one more times than the difference. That is, maximum no. 3 is written as 2+1=3 times. Then, we back, up to 1. So,  111 ´ 11111  =  1233321]