cover Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

How many triangles are hidden in this image?


I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.


    1. I hope to post the answer below a little later. So don’t read on if you’re one of those boring people who hates spoilers

    2. That’s a very obvious way of circumventing the instruction of NOT posting your answer, Dave.

    3. and now is when I admit that I actually got the right answer as in the correct individual sub-totals of triangles of different sizes but failed miserably when adding them up 😦

  1. I’ve just done a recount and got 1 more than I thought I had before. It’s slightly more tricky to count all of the combinations than I had expected.

    1. When he says dont post the answer, what is it about people like you that can’t help but immediately post the answer?

  2. I have no idea how many hidden triangles there are, but it took me about a minute to count the obvious ones.

  3. It makes a change to see this puzzle in the form of triangles – variations using squares tend to be more common (and easily lend themselves to deriving algebraic solutions once you start writing down the number of 1x1s, 2x2s, 3x3s and 4x4s – something that’s probably also possible with this triangular arrangement).

    1. Indeed, there is an algebraic solution to this type of puzzle, based on the number of mini-triangles at the bottom. 2 minutes on Google will reveal. (other search engines are available)

    1. @Richard M

      Someone has once again (above) posted in my name. It is indeed flattering to have a tribute band that wants to be me. But it is odd that they make such heavy whether of saying what I would say but saying it badly and not like I would say at all.

      In all my posts I have never posted a spoiler. I may have helped elucidate possibilities in Richard’s thought processes when there have been vageries and ambiguities. And I have helped when complex solutions have been proposed where simple intuition gets there faster (such as the simple division of buses per frequency by buses per walk to get that answer).

      But I have never wanted to spoil the answer for anyone who wanted to wait until Monday.Waiting and reading are separate things.

      The correct unspoiled answer has already been given several times. The case turns on the curious use of the word “hidden” as several have pointed out already. But can triangles be hidden in plane sight? Here the deeper philosophy starts to emerge and we may have disagreement between those who are right and those who disagree with them. That division exists everywhere in life so it existing in the comments section of a website is not to be unexpected.

    2. Here we go again. Obviously not the real me, as I would avoid mistakes such as “whether” for “weather”, and “plane” for “plain” – and I know how to spell “vagaries”.

      Last week, I was the first person to post a correct answer, so I appreciate that’s a spoiler in the modern sense of the word. I just want people to be forewarned that if they read the comments they may well see an answer.

    3. Fake Barry Goddards! Please stop arguing with each other. It is getting like Spartacus in here.

      As the one and original I say that truth cannot be spoiled. The truth is 47 triangles as the outer frame is what hides them. It is not itself hidden.

      Now perhaps we finally have an answer to the riddle: How many Barry Goddards does it take to count some triangles?

      Now all of you rest. Richard does not need you all here. Go home and found a society for people who are not called Barry Goddard.

  4. Could all of the fake Barry Goddards kindly sod off? You’re spoiling my good name so much that I’m tempted to change it to Savile.

    1. All
      Please do not spoil Barry’s good name.
      JS & SH & JK & EM

  5. It does not say don’t post “spoilers”. The request is quite clear: “please do not post your answer.” Splitting hairs on the definition of the word “spoiler” is completely unrelated to your apparent inability to follow a simple request now to share your answer.

  6. I’m probably wrong but I came up with an answer in about 15 seconds. I counted the big one, then I counted the 3 slightly smaller triangles inside of the big triangle, then I repeated that same process for the next-to-largest sized triangles, etc, etc.

  7. Sometimes a spoiler is really nifty. The spoiler I really liked was “look at Google” (I don’t feel guilty giving that spoiler since it isn’t a secret for almost any question one has). My only addition to that suggestion is to see if you can get the elegant answer (with the full methodology for getting the formula) in fewer than 3 words. I found that the obvious 3 word google query gave lots of great stuff.

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