This is the 2007 version. Click here for the 2017 chapter 07 table of contents.

"Thinking Outside the Box" with the 9-dot Problem

Here is another classic puzzle, the 9-dot problem. To a person who encounters it for the first time, it can be puzzling indeed. The problem is to connect 9 dots (three evenly spaced rows of three) with four lines, without lifting your pencil from the paper. If you do not know the solution to this puzzle, you should try to solve it now, using trial and error, before you read further.

The Nine Dot problem: connect the dots by making four lines, without lifting your pencil from the paper

Why is it "very logical" that puzzle solving often requires a low-probability response?

Again, to solve the puzzle, step outside the normal or expected pattern of responses. One must try unusual or low-probability alternatives. This is logical if you think about what defines a puzzle. A puzzle is a problem for which the obvious response does not work. Otherwise the situation would not be puzzling. So a puzzle always requires a person to think "outside the box."

In this case, the solution is to violate the common assumption that one must stay within the square defined by the dots. When you start experimenting with lines that extend outside the square, the answer usually comes quickly. Here is one solution. If the dots are numbered 1 through 9, then draw a line from dot 1 through 5 to 9, then up through 6 and 3 and beyond, then back down through 2 and 4, then right through 7 and 8.

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