If f(X,Y)=g(X,Y-1)+1, g(X,Y)=f(X-1,Y)+1, f(X,0)=0, g(0,Y)=0, find f(X,Y)

[kebot]

X,Y are natural numbers.
[h=1]What is f(X,Y), if f(X,Y)=g(X,Y-1)+1 and g(X,Y)=f(X-1,Y)+1, and f(X,0)=0 and g(0,Y)=0?[/h]I am lost a little, got a loop, like f(x-1),-1)=-2 but it does not answer my question what is f(x,y)=?

Thanks.

 

[Deleted member 4993]

X,Y are natural numbers.
What is f(X,Y), if f(X,Y)=g(X,Y-1)+1 and g(X,Y)=f(X-1,Y)+1, and f(X,0)=0 and g(0,Y)=0?

I am lost a little, got a loop, like f(x-1),-1)=-2 but it does not answer my question what is f(x,y)=?

Thanks.

Did you figure out first : g(x, y-1) = ?

 

[kebot]

Did you figure out first : g(x, y-1) = ?

No, I was thinking like as
f(x,0)= 0, here y=0. So it is equal to g(x,-1)+1.
g(0,y)=0, here x=0. So it is equal to f(-1,y)+1.

But I have no idea what I can say about f(x,y) unless both are zeros.

 

[stapel]

No, I was thinking like as
f(x,0)= 0, here y=0. So it is equal to g(x,-1)+1.
g(0,y)=0, here x=0. So it is equal to f(-1,y)+1....

What happened when you tried following the helper's hint?