Solution

Forwards Add Backwards Vihaan

First name
vihaan
School
singapore american school
Country
Age
11

It came to me when the question in between 200 and 300 was asked. why not derive a formula for n and n+100 (  100  <= n<=1800) I split it into two bounds from 100 to 900 and 1000 to 1800.

 

bound 1 (100-900) 

h is hundreds digit of n (n=100h)

 

derivation of bound 1

a+c=h (0,1,2,3,4,5)

a+c=h-1(5,6,7,8,9)

a is one  c is h minus 1 

a=2 c is h-2 

h outcomes with 5 valid digits 5h

 


 

a+c =h-1 

 

same logic but with h-1 pairs 5 valid digits so 5h-5

 

 

5h+5h-5= 10h-5

 

formula 10h-5