Problem / game
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