To find all the natural numbers which gets reverse when multiplied by 9

To find all the natural numbers which gets reverse when multiplied by 9

1089 = 33×33

1089 ×9 = 9801 = 99×99

1089 is the smallest natural number which gets reverse when multiplied by 9.

There is interesting pattern for all the numbers.

 

1089 × 9 = 9801

10989 ×9 = 98901

109989 × 9 = 989901

1099989×9 = 9899901

10999989×9 = 98999901 

10891089×9 = 98019801

 ..............  

If number of digits in number is not  multiple of 4 then only one number is possible.

10999…(n-4) times 89 ×9 =98999…..(n-4) times 01

 Where n is number of digits.

If number of digits in the number  is multiple of 4 then 1 more number is possible.

10891089 × 9 = 98019801

10891089…….1089 × 9 = 98019801……….9801

To find N natural numbers not necessarily distinct such that their sum is equal to their product

To find N natural numbers not necessarily distinct such that their sum is equal to their product

2+2 =2×2

1+2+3=1×2×3

1+1+2=4=1×1×2×4

1+1+1+2+5=1×1×1×2×5

1+1+1+1+2+6=1×1×1×1×2×6

In general,

1+1+1+…..{(N-2) times}+2+N = 1×1×……{(N-2) times}×2×N

 

The above formula was published in Ramanujan Mathematical Society newsletter in June-2014 under problem and solution section.

 

Triangle - MCQ- Class 10 - By Dr Rajesh Kumar Thakur