I was inspired to explore a popular (and possibly infuriating!) social media puzzle: How many triangles? The idea for this presentation and free MS PowerPoint triangle puzzle template came to me, because when browsing the variety of responses on Twitter, it struck me as a lesson in critical and broader thinking. In this blog, I share the puzzle itself, my thought process, and my presentation video on the subject. Additionally, I provide the ‘How Many Triangles?’ slidedeck, which you can use as a clean and simple free PowerPoint template.
I cannot teach anybody anything; I can only make them think.Socrates
How Many Triangles? Puzzle…
I created the image below using shapes, lines, text and formatting in MS PowerPoint. It is my own depiction of a puzzle you may have encountered on social media called, ‘How Many Triangles?‘. For some, it’s an intriguing and fun brain-teaser. For others frustrating and infuriating!
I invite you to have a go at the ‘how many triangles’ puzzle. See what answer you get, comment below with your approach and result.
I will then share my results and thinking below, in the form of my 18-minute YouTube video presentation. In addition, I provide a quick summary of the key points for you via this blog. You can also download the slidedeck for yourself to use the clean slide template for your next presentation.
A Lesson in Critical Thinking
Our comforting conviction that the world makes sense rests on a secure foundation: Our almost unlimited ability to ignore our ignorance.Daniel Kahneman
How did you get on? Now take a look at my video below n the context of a PowerPoint presentation. I discuss various approaches to the ‘how many triangles’ puzzle and share my results. I then discuss key lessons in critical thinking and thinking differently.
When browsing the various responses on Twitter comment thread, I noticed some common themes and approaches, for example:
- Quick appraisals or giving up
- Comprehensive mathematical equations of geometry and algebra
- Visual demonstrations and graphical explanations
- Detailed grid references and associated lookups
- Half-hearted attempts, possibly influenced by conflicting answers
Some approaches seemed mind-bending, especially the ensuing ‘battle of the maths‘; commenters even argued over whose mathematical equation was most technically accurate to explain the geometry. They were like proud cocks, each displaying their brilliantly complex plumes of algebra to get to the same result (18). It reminded me of the popular meme below, which explained my confusion perfectly! I therefore understand why many people seemed to get frustrated and/or simply post along the lines of, “Why bother?!”…
The brain is a machine for jumping to conclusions.Daniel Kahneman
Of the hundreds of comments, I couldn’t find one appearing to think ‘outside the box’ (or pyramid in this case). There are more triangles to be found beyond the usual 18 “correct” answer. But to find them, you must take a broader thinking approach to or think differently about the problem. I explain more in my video presentation about these, plus the mind-shackles I noticed people placing upon themselves. But here’s the slide where I share ideas, tools, and further reading to help develop your own critical thinking skills:
Think how comforting it is to be surrounded by people who think in the same way, who mirror our perspectives, who confirm our prejudices. It makes us feel smarter. It validates our world view… these dangers are as ancient as mankind itself.Matthew Syed
I discuss Matthew Syed extensively and share a particularly useful book of his, ‘Rebel Ideas: The Power of Thinking Differently‘. Moreover, Matthew is a guru on cognitive diversity; I really like his approach, and he also shares many fantastic ideas on the importance of building diverse teams. ‘Diversity’ isn’t about pigeonholing people into categories and quotas of race, sex, orientation, and other protected characteristics; it really comes down to achieving diversity of thought. I also mention other thinking tools and recommended reading, which I share below:
- Matthew Syed: Take a look for example at his ‘Rebel Ideas‘ book on thinking differently. However, I’d also happily recommend his others, such as ‘Black Box Thinking‘ and ‘Bounce‘. He’s a great author and shares some fantastic concepts to help you excel at the office and in general life.
- De Bono Thinking Hats: I find the following article a really informative take on the De Bono thinking hats. Though viewed through the lens of policing and promotion, you can interpret the thinking tool for any problem. In addition, it’s a useful angle for advancing your career or CPD decisions.
- Daniel Kahneman: Here’s a link to his book, ‘Thinking, Fast and Slow‘. You might also like his more recent publication on clearer thinking and problem-solving, ‘Noise‘.
- Marcus Aurelius: Want to take a more philosophical perspective on life? If so, ‘Meditations‘ stands the test of time.
- I also mention the book ‘Did You Spot the Gorilla‘ by Richard Wiseman. This is another worthwhile read and more about recognising opportunities; a key tool to unleashing your mind shackles.
A reliable way to make people believe in falsehoods is frequent repetition, because familiarity is not easily distinguished from truth. Authoritarian institutions and marketers have always known this fact.Daniel Kahneman
‘How Many Triangles’ PowerPoint Slide Template
Finally, here’s the actual slidedeck should you wish to download for your own work my clean, simple slide template. Naturally, I call it ‘How Many Triangles’…
I hope you’ve enjoyed this puzzle, thought experiment and presentation. Please like and share with others who might find it useful. If you like what I do, you can support my work to help keep free content flowing; all coffee donations greatly appreciated! Want me to create fantastic, time-saving templates just for you and your business? Then please get in touch to arrange a bespoke quote. Finally, feel free to leave your feedback below and comment what you’d like tutorials and templates about in future.
Kind Regards, Adrian