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Draw 4 lines through the dots - solution

Draw 4 lines through the dots problem

Have a go at the problem, and it may seem impossible.

The solution is on the right. When you look at it carefully, you will see that the lines don't stay within the grid of 3 by 3 dots. They go "outside the box".

The phrase "think outside the box" means "Don't just think of the obvious solutions. Try thinking of weird things; they might help you to solve the problem." This is a very useful technique, both in solving difficult logical problems, and in being creative. I'm not sure if this puzzle was the origin of the phrase, but it fits it perfectly. It's not that you think you have to keep your lines within the box of dots; it just never occurs to you to go outside (and I shouldn't say "you", as I did exactly the same when I met this puzzle.) The limitation in thinking is so strong that your reaction to the solution is probably "That's cheating!" But it isn't. The original problem was carefully worded as "draw 4 lines through all the dots", not "join the dots".

solution to dots puzzle

So how do you "think outside the box"? That's a hard trick to learn. Doing these types of puzzles can help. Even if you can't solve them yourself, trying, then understanding the solutions, can loosen up your thinking, so you start trying to think sideways rather than directly. Look at the wording of puzzles or problems. Have you understood them correctly? What do the words actually mean? If you describe the problem for yourself, is there another way of describing it which might give you other ideas? Another point is to stop your thinking going round in circles. If you're trying the same failed solution time after time, then give yourself a jolt, and try something else!