A big hello to all the new people who have been kind enough to follow me on Twitter – almost up to 14,000 now!

Here is this week’s puzzle …

Can you create 8 equilateral triangles with just 6 matches?

Update: You are not allowed to break the matches! Also, what is the greatest number of equilateral triangles you can make with the matches?

As ever, please do not post your answer, but do say if you think you have solved it and how long it took. Have a great weekend and i will see you next week.

1. * says:

Yes, few minutes.

2. It’s the one where we think in more than 2D:) But I only got 6 so far

3. Egon E says:

Hmm, about a minute to solve it…

Here’s a different one – 4 equilateral triangles with 6 matches without crossing them.

1. * says:

No problem:), but this one is 3D.

2. Nick Sharratt says:

This one I can do, took a few seconds. thinking tails not heads 😉

but can’t see the answer to the main one yet. 😦

4. Simon says:

I hate these puzzles, because the rules aren’t clear (although I’m pretty sure that I have the ‘correct’ answer). Equilateral triangles live in the world of geometry, matches don’t. Can we break the matches, superimpose them, cut them up into Cantorian dust? I’m thinking that the ‘correct’ answer has twice as many triangles as the answer that doesn’t contain as many physical objections (if that’s not giving away too much)…

5. Roland says:

There’s no restriction on breaking them, so in theory you can make any amount of shapes

1. Garrett says:

Excatly. You could break them each into 5 pieces and end up with 27 equilateral triangles, or split them each into 14 pieces to get 118. But I don’t think this is the solution he’s looking for.

6. Kevin says:

2 minutes with pen & paper. 2D, no breaking.

1. Simon says:

but do the matches lie flat? ie are they true equilateral triangles?

2. How does “not lying flat” mean “not equilateral?” An equilateral triangle simply is a triangle with all three sides the same length, regardless of dimensionality.

7. Eve says:

about 3 mins? only with pen and paper, and I only got it so quickly because of cultural learning.

8. I got a solution in just seconds. Oy vey! Perhaps all these puzzles are sharpening my problem-solving skills. (Or maybe I just got lucky.)

I think some people are overthinking this. My solution is 2D and involves no breaking. (Though I’m curious to see how Simon solved it.)

9. Fergus Gallagher says:

oi vey

But can you make just 4?

10. Jim T says:

Yay I did one. Couple of minutes

11. Curnir says:

Done it in a few seconds. Now trying to solve the “4 equilateral triangles with 6 matches without crossing them.” puzzle

done the second puzzle to0.

Nice one. Got it quickly as did my 10 year old daughter.
But could any friends called David get it?
Plato helped me with the 6 matches 4 triangles.

14. TS says:

Can I use a lighter instead?

1. * says:

15. Jareth says:

Easy as heck. The time it took to read the question.

16. JN says:

I think I got it right in a about one minute with the help of pen and paper as well.

17. Michael K Gray says:

No.

18. Wow finally a Friday Puzzle I managed to do! (Saying that I have probably got it wrong now!)

19. Joao Pedro Afonso says:

Few seconds and 2 drawings away… yes, easily solvable.

I’m intrigued by what you asks… “how long we took?”… the idea is to gauge population’s subjective time? How many dead ends in average we experience before the final solution? Or it would be interesting to count the time we took effectively? But then, no one would be able to connect the times to correct answers (someone who’s said has found it, maybe has not). Lateral thinking like’s Simon is also interesting (actually, my first reaction before pick a paper was to break the matches) because some puzzle are solvable by bending the rules we thought there was there… the question is when to bend them or not.

20. maarten says:

i can make 10 🙂
which includes 8
took me a minute or 5 though

1. maarten says:

let me change that into 13…
but that still includes 8

21. Ania says:

Less than 10 seconds. Easy peasy!

22. DeepField says:

About 5 seconds for the first question. Still thnking about the second…

23. Rob says:

There are some star problem solvers here

24. Gevalt! This one seems to easy…I think I got it in a few seconds (first thing that popped in my head)….

25. * says:

But not re beating the chimp… why noone wants to give it a trial? It requires miliseconds! And is really difficult even if you don’t have to think too much.

26. Took me a few minutes ’cause I had to find some matches…. no pen or paper….. just matches….lol…..giggle…..

27. Five seconds for the first question. Don’t want to think about the possibilites that arise if I’m allowed to break the matches…

28. Bruce Bignell says:

< a minute with paper and pencil… Me likey

29. Richard Strand says:

I didn’t break any matches and it took about a minute. The solution makes me feel quite festive!

31. salomeuk says:

‘Update: You are now allowed to break the matches! ‘ – I assume that should be NOT, rather than NOW?!

32. ivan says:

There are much more difficult matchstick puzzles than this one.

33. rolak says:

Almost instantaneous. But I have no idea about the max # of equilaterals, i.e. wether there is a possibilty of >8.

34. lflcorreia says:

About a minute with pen and paper to solve the first question, without breaking any match but getting 2 big triangles of the same size plus 6 smaller ones with the same size. Don’t know yet the answer to the 2nd question.

35. Michael K Gray says:

Yes.

36. Jane says:

took a minute or so for 8

37. Just a couple seconds for 8. I think my answer to the second one is also “8.”

38. slightly skeptical says:

One minute.

39. I’ve enjoyed your posts and have embedded one of your videos (Top 10 quirky science tricks) in my blog 🙂

Regards!

El Gonzi

40. Joao Pedro Afonso says:

Wow, for the second question. Now, that’s a nice twist considering how many triangles people are saying they achieve. I’m really interested to see the solutions they came through because I think I can prove that 8 is the maximum number of triangles we can achieve in the plane (It’s not that complicated to reach there and from it, the number 8 as the cube of 2, will came naturally). So, what I overlooked?

A different question is how many ways of building those 8 triangles there are. Obviously, if we deem different two ways where the triangles are of different size, then the number of those ways are infinite. But if we cater for a different criteria, for example, how the triangle’s apexes might be oriented, then the number might be finite. To proceed further, that criteria would have to be established.

41. Cosmin Romania says:

I thought I found a 6 triangle solution, but actually there were 8. 😀

42. Kim Laursen says:

43. jw nielsen says:

yes, a minute or so.

44. Javier says:

Got it in about 30, seconds… 2D, very simple

45. Samuel Willcocks says:

rather under half a minute. I had paper-and-pencil ready as usual for the Friday Puzzle, then once I had read the puzzle I thought it would be better to go to the kitchen and get a matchbox. I had then solved the puzzle before even rising from my chair – it was the thought of the matchbox that did it!

46. Spy says:

Took me just long enough to draw 6 lines to move my solution from visualizing it to verifying it.

47. Zaq says:

not “equilateral” but i did it, not too long, though i guess you could say i “cheated”

48. Zaq says:

well, now i have it without cheating….

49. ldr says:

when i read the text, exactly 5s

50. christina says:

Just a few minutes but I had to draw it out first.

51. Michael says:

Believe it or not, this was curiously easy…. 16 seconds, and that’s total time of getting pen and paper and drawing it out… now for more configurations…

52. Anonymous says:

try 12 sticks to make 8 triangles

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