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 $31$.

I like tricking my friends with this one:
$S_n(\mathbb R) $ denotes the set of $n,n$ real symmetric matrices
$ S_n(\mathbb R) ^{++} $ denotes the set of positive definite matrices. 
$ S_n(\mathbb R) ^{--} $ denotes the set of negative definite matrices. 
What are the path-connected components of $S_n(\mathbb R) $? 
They all answer $ S_n(\mathbb R) ^{++} $ and $S_n(\mathbb R) ^{--} $. 
This is clearly wrong since $S_n(\mathbb R) $ is a vector space. 
