I am interested in the problems where the formulation of the problem has some kind of mistake in it and as a consequence gives unexpected answer.

Can't explain it better than this example:

For example: $4^2 = 4 \cdot 4 = 4+ 4 + 4+4$ (sum $4$ times) Similarly: $$\frac{d}{dx}x^2=\frac{d}{dx}(x\cdot x)=\frac{d}{dx}(x+x+...+x) = 1 + 1 + ... + 1 = x$$

Since the $1$'s are summed $x$ times. I hope you see what went wrong :) If you have encountered problems of this type, please share.

**EDIT:** I am aware that my proposed example has a mathematically inconsistent step, this type of expansion is only allowed for natural numbers making the function non-differentiable. However this is the kind of inconsistencies I find amusing.