On Friday I posted this puzzle…
coverCan you circle exactly four of these numbers such that the total is twelve?



If you have not tried to solve it, have a go now.  For everyone else, the answer is after the break.

You turn it upside down and do this…..


Did you solve it?

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. In creative problem solving, everything’s allowed as long as it leads to a correct answer… 😉 I got the answer, but found the wording a bit ambiguous – “circle four numbers”, to me, reads like one circle around four numbers, not four circles around one number.

  1. I didn’t get it. So obvious… maybe I was distracted because we weren’t allowed to post comments on Friday. And now we are.

  2. I don’t even consider these kinds of puzzles as legitimate. I mean, if you’re going to just throw the rules out of the window, how are you supposed to decide which rules to throw out in the first place? In the initial puzzle you are faced with two distinct numbers and asked to circle four of them, if you’re okay with changing the numbers by turning them upside down, then the original puzzle is meaningless – you’ve just decided one way of breaking the rules is okay and not others. Another solution would be to draw a circle, circle that circle (considering it a zero) then circle two sixes You’d have drawn 4 circles and circled numbers adding to 12. It’s an equally valid “pointless logic” to the actual solution.

  3. If you had stipulated that the numbers were written on a piece of paper, then that would have been reasonable. As it is – how can you turn pixels on a web page upside down? Is that a standard feature of web browsers that I’ve been missing? Should I stand on my head, should I turn the monitor upside down, should I print the damn thing out and turn that upside down?

    1. Come on. You can’t circle the numbers while they’re in the browser to begin with…unless you scribble on your monitor, or import the image into a program that allows you to draw circles…which is also taking it out of the web browser. I think “circle … numbers” reasonably implies imagining the numbers are on a piece of paper.

      It was a stretch, but I don’t think the puzzle was unreasonable. I got it…and so did several others.

    1. I didn’t answer the question till this morning (10 seconds) in case Richard decided to change it to another question as he did last week.
      Of course, there is nothing to stop him changing the question now and making us all look like idiots. (OK, most of us are idiots anyway).

  4. Some with the same name as me has already posted. But this is my answer.

    I circled four of the ones. Then tilted/folded the screen so it read XII. That is twelve in Times Roman font.

    I think another answer is an infinitely huge circle centered approx on the other side of the universe. This will encircle some of the corner numbers but not all of them if appropriately slanted.

    Circles that overlap may also solve the puzzle provided a double overlap cancels out.

    So thus there are many creative solutions to this puzzle. Those who’s creativity failed them should not be complaining as such,

    1. That’s weird, because someone with a different name from me has already posted above.
      What a spooky coincidence.

    2. @Slange Navarr Thank you for your kind words and support. Being able to see further and deeper than others is not always appreciated. Often when I see new horizons others just see culdesacs.

      @Gabby Bollard Star charts are much more than just stereotypical Sun charts. A deep study of the art will repay many times over. Mocking just leads to ignorance.

      There are many answers to the puzzle, I am humbled to have been able to contribute several that other’s have not previously thought of.

  5. Doesnt say 1 circle, just to circle 4 numbers. I encircled the first 2 numbers on the first 2 lines. Done.

    1. If you consider that every ‘I’ is a spitting image of a vertical bar and looks nothing like a ‘1’, you only have to circle four sixes to leave two sixes adding up to twelve.

      On the other hand the sixes look more like upside down nines than sixes.

    2. Stu, yours is the best answer. richard never specified that the total had to be the total of the numbers inside the circles.

    1. alas, this approach fails because the problem requires you to circle four “numbers.” |6| is just one number, not three.

  6. I don’t understand why so many are upset by this. With the image the “right way up” there is no correct solution (regardless of the size of any circles) so the only variable must be the aspect, i.e. rotate the image 180º. Job done. I did it in less than 60secs, but certainly not immediately; I had to go through the foregoing logic to get there.

    As for rules it’s the same as how the Law works. If it doesn’t say you can’t, you can.

  7. I had that answer, by not using the screen, but a piece of paper.
    Just like writing 1000 by folding a piece of paper.

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