Question 165
We are looking at numbers for which two adjacent digits always add up to the digit immediately to their right (if it exists). So two adjacent digits when added together are always smaller than $10$, except possibly the last two digits. Furthermore, the first digit cannot be $0$. An example of such a number is $1347$, because $1+3=4$ and $3+4=7$. How many such five-digit numbers do there exist?
A) 1
B) 2
C) 3
D) 5
E) 8
A) 1
B) 2
C) 3
D) 5
E) 8