This page provides extra material for my book on creativity for writers – Opening the Creativity Diamond. Here you will find more information including the answers to the various Outside the Box problems in the book. I also hope you’ve found my book useful – please do leave a review on Amazon or goodreads, even if you thought the book could be better.
If you simply want the answers to the Outside the Box puzzles then scroll down to the links, if you want a reprise of the puzzle, carry on!
The 9 dot problem
In my book I discuss the classic problem of joining a grid of nine dots with fewer and fewer lines. I showed you how to do 5 lines and 4 lines and also hinted that it is possible to go further. I gave some clues:
How thick are the lines? They do not have to be one-dimensional infinitely thin lines
How big are the dots? They don’t have to be mathematically precise zero size points
How flat is the paper? Who said it was a sheet of square paper laid on a flat surface?
So here’s a solution for five lines:
There are several ways to make this work and this is just one of many. There are alternatives such as doing the lines row by row – I happen to prefer spiralling in on the solution.
One thing I find interesting is that my natural preference is for the lines to not overlap – this isn’t a constraint of the problem just how I choose to solve it.
As I say, there are many solutions.
Now one for four lines:
This is the classic outside the box where the trick is to draw lines ((2) and (4) on my picture) that extend beyond the boundaries of the box. Although the order is arbitrary I find it easier to remember to start with line (1). By using ideas from the two line solution (see later) you can create many alternate solutions to this problem but they are far less elegant.
If you got this solution the first time you saw it then you should congratulate yourself – I’ve known this solution for years and don’t know when I first learned it.
I don’t think I can claim to have solved it without some help!
Of course you really want to know how the answers to the three, two, one and even zero line versions – here they are on new pages, each one explained. I give them non-numerically as this is the order I found solutions to them. The solution for two lines was produced on a training course I ran – it’s a legitimate solution but, perhaps, less elegant than the others.
Do feel free to let me know of other solutions!