Solutions to the nine-dot problem

This is the classical four-line solution, the arrow could of course point in three other directions. To come to this solution, you would maybe not need to think outside the box, but surely outside the square.

A three-line solution to the nine-dot problem is actually quite simple. Nowhere is stated that the lines need to pass through the centre of the dots, so a simple three-line zigzag pattern would do it.

nine-dots-solution2

The above four- and three-line solutions, could be deduced through a trial-and-error approach, but doing it with only one line, would require stepping back and out of your normal thinking habits to find new and surprising solutions, what Edward de Bono calls “lateral thinking”.

Below are a few alternatives, but I would appreciate any further suggestions.

1) Cut out the nine dots and glue them in one line on a piece of paper, then draw your line through them. Nothing in the challenge prohibits you from that.

2) Take a paint brush and connect all nine dots with one broad stroke covering all of them.

3) Burn the paper and spread the ashes in one line for you to draw through.

4) Make the paper into a cylinder and connect all nine dots with an oblique straight line. This could also be done at a grander scale on a flat piece of paper, with an (imaginary) line going three loops around the world.

nine-dots-solution-3
Source: Archimedes-lab.org

5) And finally, my favourite, the origami method.

nine-dots-solution-4
Source: Archimedes-lab.org