[Miss Jordan]

Nine Dots




Here are nine dots arranged in a square matrix. Can you draw four straight lines, without lifting your pencil from the "paper," through all nine dots?

Answer:


You should probably have figured out the answer on the right. This is a well-known example of lateral thinking, thinking outside the borders in this case.
Using even more radically lateral thinking, here is a
solution with only three lines. Since I said "nine dots," this would seem to be a valid solution (better than the four lines that I asked for). But, had I called them "nine points" instead of "dots," this solution would not be valid (since points have a zero size). In that case, you could possibly argue that three parallel lines would work, meeting at infinity. But you would have trouble drawing them. And there are logical problems (self-contradictions) with saying that parallel lines meet at infinity.
An even better solution is to use a very wide pencil, and draw a very wide line through all nine dots in one stroke. After all, I did say "dots" and "pencil."