A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $$\frac{1}{4}$$. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is/are on the path of the man?

The equation of a line in intercept form is $$\frac{x}{a} + \frac{y}{b} = 1$$, where $$a$$ and $$b$$ are the intercepts on the coordinate axes.

The arithmetic mean of the reciprocals of the intercepts is given as $$\frac{1}{4}$$. So $$\frac{\frac{1}{a} + \frac{1}{b}}{2} = \frac{1}{4}$$, which gives $$\frac{1}{a} + \frac{1}{b} = \frac{1}{2}$$.

Now we check which of the given points lies on the line $$\frac{x}{a} + \frac{y}{b} = 1$$.

For point A$$(1, 1)$$: $$\frac{1}{a} + \frac{1}{b} = \frac{1}{2} \neq 1$$, so A does not lie on the line.

For point B$$(2, 2)$$: $$\frac{2}{a} + \frac{2}{b} = 2\left(\frac{1}{a} + \frac{1}{b}\right) = 2 \times \frac{1}{2} = 1$$. So B lies on the line.

For point C$$(4, 4)$$: $$\frac{4}{a} + \frac{4}{b} = 4\left(\frac{1}{a} + \frac{1}{b}\right) = 4 \times \frac{1}{2} = 2 \neq 1$$, so C does not lie on the line.

Hence, the correct answer is Option C.