Question

A function f(x, y) is defined for non - negative integers
I. f(0, 0) = 0
II. f(2x, 2y) = f(2x + 1, 2y + 1) = f(x, y)
III. f(2x + 1, 2y) = f(2x, 2y + 1) = f(x, y) + 1
What is the value of f(11, 5)?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

f(11, 5) = f(2 $\times$ 5 + 1, 2 $\times$ 2 + 1)
= f(5, 2) = f(2 $\times$ 2 + 1, 2 $\times$ 1)
= f(2, 1) + 1
= f(2 $\times$ 1, 2 $\times$ 0 + 1)
= (f (1, 0) + 1) + 1
= f (1, 0) + 2
= f (2 $\times$ 0 + 1, 2 $\times$ 0)
= (f (0, 0) + 1) + 2
= f(0, 0) + 3
= 0 + 3
= 3