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 $31$.

Question 1)
You are building a straight fence 100 feet long. There is a fencepost every 10 feet. Fence panels are 20 feet long.
How many fence panels do you need?
How many fenceposts do you need?
Question 2)
You are fencing a rectangular area 100ftx100 ft. There is a fencepost every 10 feet. Fence panels are 20 feet long.
How many fence panels do you need?
How many fenceposts do you need?
Folks often forget that the corners are special and count wrong, especially when presented with the first question immediately before the second.
