ISI2015-MMA-36

Question

For non-negative integers $m$, $n$ define a function as follows

$$f(m,n) = \begin{cases} n+1 & \text{ if } m=0 \\ f(m-1, 1) & \text{ if } m \neq 0, n=0 \\ f(m-1, f(m,n-1))  & \text{ if }  m \neq 0, n \neq 0 \end{cases}$$ Then the value of $f(1,1)$ is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

f(1,1)=f(0,f(1,0))   since m$\neq$0,n$\neq$0

=f(0,f(0,1))           since m$\neq$0,$n=0$

=f(0,2)                 since m$=$0

=3                       since m$=$0