Tell me problems that can trick you I am looking for problems that can easily lead the solver down the wrong path.
For example take a circle and pick $N$, where $N>1$, points along its circumference and draw all the straight lines between them. No $3$ lines intersect at the same point inside the circle. The question is how many sectors do those lines divide the inside of the circle into. First it looks like $2^{N-1}$, which is true up to $5$ points, but with $6$ there's only $31$.

When asked to answer fast, in my experience people usually fail at this one:

$$P\implies \neg P\,\,\,\,\text{ tautology or contradiction?}$$

