Tuesday, 17 August 2010

Creative Thinking Challenge Follow-Up

During the summer I read a fairly interesting book, Think! Before It's Too Late, by Edward De Bono. Brief review of the book below.

In one section on creative thinking in 'Knowledge and Information' - just after being quite negative about multiple choice exams, something I've reflected on before, (here) and (here) - he poses a couple of challenges. One of these challenges was the basis for the Creative Thinking Challenge I posed.

Go read the comments to the above challenge to see the different approaches - I give a brief view on the approaches later in this post.

My Approach
My approach was to adapt the "Gauss method" and apply it to even numbers. After experimenting a little I was able to see the pattern for even numbers. So, my approach to the problem...

First listing the two rows, one in ascending and the other in descending order:-

    2   4     6   ...  298 300
300 298 296 ...    4     2

finding the pair sums (300 + 2, 298 + 4, etc) all summing to 302, noting that there are 150 such pairs and that the sum will be double the required amount, so I must divide by 2. Giving

(302/2) * 150 = 151 * 150

As for the mental arithmetic, well I took 15*15 to equal 225, then added a couple of zeros (one for each one I'd removed from 150*150 - ie divided by 100 before, so I must multiply by 100 afterwards), giving 22500, then I must add the final 150 (to get to 151*150) giving 22650.
(we all know our 15-times table right? 
I, for some reason, know it's 225, but doing it long-hand in your head (?) would be 15*10 = 150 + 10*5 = 200 + 5*5 = 225)
This method is the so-called Gauss 'trick' or method. 

The Gauss Method?
I saw a suggestion (on twitter I think) that this was the famous Gauss problem, a problem that he is supposed to have solved as a school child.

I found a reference that apparently shows the first known solution to this type of problem was presented by Alcuin of York; a translation from the Latin of the problem and solution are (here) - it's the one about the doves on ladders!

The Challenge Answers
Firstly, many thanks to those that took up the challenge and were willing to submit their answers! It was really interesting to see the different trains of thoughts. There were some different and inventive solutions - and that's what it's all about.

The first effort came from Trevor Wolter. I think he took the approach that I would've taken if I hadn't known the 'trick'. He wrote out a few observations, looked for a pattern, came up with a hypothesis and presented it. Right answer!

The next entry from anonymous either knew about the formula for arithmetic progressions or looked it up. He/she then presented the modified version. I assume they tried it out. There is potential for mis-interpretation in the formula though -  the 'n' value must be the highest even value in the series. If I'd said add up the even numbers from 1 to 301, there would be some pre-filtering needed.

Next up was Timothy Western, who presented a simple logic case and then did the actual calculation with the aid of excel. Short and sweet - right answer!

Abe Heward gave a close rendition of the "Alcuin of York" method. Creative thinking and right answer!

It looked like the arithmetic progression angle was the basis for Stefan Kläner's answer. Right answer!

The "Alcuin" approach was in use by Ruud Cox - well demonstrated steps and the right answer!

The arithmetic progression approach was used by utahkay. Right answer!

Finally, Parimala Shankaraiah gave a detailed walk-through of the initial observations, spotting patterns, following a hunch about arithmetic progressions, looking that up, modifying the formula, trying that out and matching with the observation to present the final hypothesis. Good analysis, research and explanation. Right answer!

What's interesting about these answers is that there are different methods of approaching and solving the problem - there are no right or wrong approaches. I found this problem intriguing purely from the "creative thinking" or angle - this is something that can be practised, to add as another tool in the testing toolbox. Something I'm going to explore more.

Another good point about showing your thinking is that it's a natural step for writing bug reports. So I reckon a lot of the answerers can write bug reports with enough detail.

Book Review
The book is part complaint on the current state of thinking, part re-hash of previous work and part self-promotion. A fairly ok read but I do have quite a few niggles with it. The book has had mixed reviews - although I read it quite avidly, which is slightly unusual for me!

There is a repeating statement through the work: Good but not enough. After a while it grates a bit. I understand his point and perhaps the continued repetition is the "drilling it home" method, but I'm not always receptive to those types of approaches.

The book gives short summaries of his previous work on Lateral Thinking, Six Thinking Hats and Six Value Medals. The summaries are fairly superficial - in theory not enough for someone to pick up and use in depth, although not impossible to grasp and use at some basic level.

Another niggle I have with the book is the lack of references or bibliography. De Bono states that this is because all his ideas are his own - however he uses Gödel's theorem to state a point about perception without referencing the theorem. Some references and bibliography would be nice, otherwise it just comes across as opinions without the back-up.

There are some reasonable points made, but when they're not backed up by references to the source material the reader has reached a dead-end in this book (if he wants to dig deeper into the source material).

I haven't read any previous De Bono work - I'll probably delve into the Lateral Thinking work at some point, but for now I have some pointers.

More on some creative thinking reflections connected to this book in another post.

Getting inspired about creative thinking for testing?

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