Thinking Outside The Box

Driving You Dotty
Part One

Recently I went on a departmental training and bonding trip to Northamptonshire. On the first night I performed in a scheduling based micro-musical with songs based on the works of Abba. The evening was filled with singing and dancing, getting to know our colleagues from London who we rarely get the chance to meet.

What has this got to do with lateral thinking, well think a little outside the box and I will show you.





The second day was a more sober affair, or at least a mildly hung over affair, looking at how to become more creative in our jobs. Building schedules isn't something you would immediately associate with creativity, but learning how to think through, and possibly around problems is an important skill.

One of the topics of the day was lateral thinking, learning ways of finding a solution to a problem without tackling the problem straight on; that is your challenge for today thinking outside the box as it were.

I am going to relate to you a puzzle and give you the chance to solve it, then in your moment of triumph I am going to make the puzzle more challenging, several times. The task is to further improve your thinking skills to get better at the puzzle.

---

Lateral Thinking

Driving You Dotty - Part One

For this puzzle you will need a piece of A4 paper and a pen or pencil. If you want to be neat a pair of compasses or a coin to draw around will help.

You need to draw a circle, about two centimetres in diameter in the centre of your page. You can then add eight more circles, the same size around it to form a square. Each circle should be about three centimetres apart.

Nine Dots

You will revisiting this document a lot, so you might like to photocopy it a few times. Alternatively go over the circles in marker pen and then continue the puzzle in pencil, allowing you to erase your mistakes.

We will start then with a very simple puzzle. You must draw four lines on the diagram. The lines must be perfectly straight, as if drawn by a ruler. Between them the four lines must contact every one of the nine circles.

This shouldn't take you long, but make sure to draw out the answer, as the puzzles get harder you may want to revisit previous correct answers.

---

Here is one answer of many possibilities.

Although this is a simple puzzle it is important to make sure you understand the solution at each level. It is through the understanding of the simpler puzzles that you will be able to supply solutions of your own for the more difficult ones.

---

OK, so that was simple, there were very limited restrictions on what you could do, and you probably found more than one solution. Some of you may even have solved it in three lines and think you are a step ahead. However there are a couple of problems with that route. 

Firstly, I specified four lines, so if you only drew three you didn't find a correct solution. Secondly, in the next step of the puzzle I am not going to reduce the number of lines you get to solve it with. Instead I have a different restriction for you.

---

Lateral Thinking

Driving You Dotty - Part Two

Return to your blank diagram and start again. The first part of the puzzle remains the same.

You must draw four lines on the diagram.

The lines must be perfectly straight, as if drawn by a ruler.

Between them the four lines must contact every one of the nine circles.

No circle should be crossed by more than one line.

---

Here is a possible solution to the problem, again it is one of many but hopefully you can see that the solution to the first variation has had to be finessed or altered to work correctly with the new restriction.

This is of course not where we are leaving this puzzle. Here is a third variation again with a new restriction to add, and I still wont be taking any lines away. Instead, I shall be giving you an extra one.

---

Lateral Thinking

Driving You Dotty - Part Three

Return to your blank diagram and start again.

You must draw five lines on the diagram.

The lines must be perfectly straight, as if drawn by a ruler.

Between them the five lines must contact every one of the nine circles.

No circle should be crossed by more than one line.

You may not lift your pen from the paper. 

---

Here is my solution to the problem, there are fewer possibilities than in the puzzles before, but this one works perfectly well.

With the new restriction you have to think differently about how to cover the necessary ground, there are enough lines, but only if you connect them in the circles. Things are about to take a turn for the tough now as I set the puzzle that was actually covered in the training. On the scale of inside the box, to outside the box, this one is wrapping paper.

What's more, the extra line I so graciously gave you to use, now I am taking it away. You must complete this variation with just four lines.

---

Lateral Thinking

Driving You Dotty - Part Four

Return to your blank diagram and start again.

You must draw four lines on the diagram.

The lines must be perfectly straight, as if drawn by a ruler.

Between them the four lines must contact every one of the nine circles.

You may not lift your pen from the paper.

---

Take some time to think about a solution to the puzzle, and make sure it meets all the restrictions. Well practiced puzzlers might want to consider whether there are alternate solutions.

Next time we will be applying further restrictions to the puzzle and paring down your options until you will be truly thinking outside the box.

Until then, keep puzzling.