The following equation is obviously wrong:


1) Can you add 4 lines to make it correct?


2) Can you add 3 lines to the equation and make it correct to six decimal places?

As ever, please do NOT post your answers, but do say if you think you have solved it and how long it took.  Solution on Monday.

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. Got 1 straight away. Haven’t got time to sit and ponder 2. Can also add just one line to make the equation correct.

    1. If you make it an inequality it isn’t an equation anymore – so not a solution as the problem asks you to make the equation correct.

      But you could use your four lines to just cross out the 3s and the 5s. Not THE solution that’s being looked for, but A solution all the same.

  2. First one seems way too easy, I cant even begin to know what to do with the second one. Old Wiseman is known for his tricks though…

  3. (1) 30s
    (2) 5 minutes to get the gist of it. I had a hunch, then found a matching solution. Convincing myself that the notation is acceptable.

    Nice one. For once, real math is involved 🙂

    1. … Hmm, national education differences will make (2) rather hard to solve for many people, or at least hard to complete.

  4. I was about to say “I know what I’m trying to do for 2 but I can’t see how to do it” but as I began typing I saw the solution.

  5. I can add four lines to make it correct

    I can add four lines and make it correct to seven decimal places
    I can add two lines and make it correct to six decimal places (although the notation’s a bit odd)

    I can’t see how to add three lines and make it correct to six decimal places.
    I must be missing something obvious for the three lines solution, but I can’t spot it.

    I can, of course, make it correct with just one line.

  6. You could also cheat and do it in one line as N = 113355. And this is why these puzzles annoy me – the easy correct answers surely aren’t the ones being looked for.

  7. First one in 20 seconds, second one immediately. It was the “to six decimals” that gave it away. Once you know what number it is, it’s easy to see how to form it, and easy to validate that your answer is correct because the 7th decimal isn’t what it’s supposed to be.

  8. i) about 5 secs

    ii) about 5 minutes

    There is also a 2 added line solution which is accurate to 5 decimal places

  9. First one took about a minute.

    Second one, I must have missed something obvious but I’ve got it accurate to 310 places using 3 lines. That took about 5 minutes.

    1. Indeed, because the obvious answer is correct to 6 decimal places and no more. I look forward to seeing what your answer is next week.

    2. 310 places, and no more? Do you mean the 311th digit in your decimal answer is the first incorrect digit in your answer? I’d like to see that.

  10. 1) Easy – about 20 seconds. It helps that each pair of digits has a gap between them, as though the puzzle was constructed in reverse (i.e. the full equation written down, then four lines removed)

    2) No idea – I’m guessing it involves adding three lines to the complete equation in (1) as opposed to the incomplete equation, but I can’t figure out how to do it. There doesn’t appear to be any mention of adding a decimal point or moving any existing lines, which makes it harder. It’s probably something either very sneaky or involving something other than standard +-/*.

    1. The grouping helps with the first problem and may hinder finding the solution to the second. So a bit sneaky. Uniform spacing would have been fairer.

  11. I immediately knew what (2) was about, took me a minute or so to work out how to implement it. I think it is one of those things that would be very hard without some prior knowledge. It took a little longer to work out what (1) was about.

    1. Actually, come to think of it, my solution(s) to (2) really require 4 lines. Though I can see a way that sort of takes 2 lines. I haven’t really found a way to organise it properly with just 3.

  12. got 1) instantly and 2) after reading Michael Sternberg’s comment above. It reminded me of something we do differently in Germany – I had to check the English way on google, then managed to solve it in less than a minute.

  13. #1: 1 minute
    #2: i know what I’m searching for, but i don’t know how to get there in 3 lines. i got there in 5 lines.

  14. Two minutes to find two solutions to #1, 5 seconds for #2. Both of course have a large number of trivial solutions as others have mentioned.

  15. I did it! I did it! Both of them. I almost gave upt oo.

    1 – 30 seconds
    2 – 5 minutes.

    Really liked this one.

  16. I Got 1) in probably a minute or so, fairly straightforward. 2) has got me completely stumped though… I’ll come back to it later, that usually helps.

  17. 1) straight away. Thought I had 2 in a few minutes, but realised I’d used 4 lines. I have to be on the right lines though, otherwise it’s a bizarre coincidence. I’m stuck now though.

  18. The first took me about a minute. I did start out on the wrong tack but saw a different way to use the lines.

    Still working on the second after five minutes.

  19. #1 A couple of minutes

    #2 Not sure about the interpretation, but I got several answers that I think satisfies the question.

    Does correct to six decimal places mean that the seventh place can vary (keeping in mind rounding)?
    for example 9.1234561 = 9.1234562 to six decimal places.

    1. Or does “correct to six decimal places” mean the formula that results in 9.1234562?

  20. Got it (part b). I remember seeing this trick in Martin Gardner’s “Scientific American” column over fifty years ago!

  21. Note for those who alter the operator to a not-equals, greater-than-or-equal to or greater-than or equal to, that would mean the result is not an equation which, by definition, requires an equality operator.

  22. Second one stumps me. At first I got it to 4 decimal places. Then I made a breakthrough and got it to 5 decimal places. Still thinking about how to get it to 6.

    1. Hahaha. I figured out an answer that lets me calculate it to something like 50.000 decimals, but I still can’t come up with one that would make it exactly 6.

    2. I may have had my symbols mixed up, so it doesn’t work after all. I’d need 3 lines and a dot for the 50.000 decimal solution.

    3. Finally found a solution that actually works. It was a very clever puzzle, and a lot of fun to solve. Caused me a bit of insomnia though.

  23. According to one definition in a dictionary, a line is a thin, continuous mark, which opens up a whole new set of answers.

  24. I have 2 solutions for part 1. I have one correct solution for part 2, but I don’t think it’s what Richard is looking for, since my solution is correct for… much more than six decimal places.

  25. First one was quick and clean….
    Second one had me playing with a pen and paper most of the day. Then the clouds just lifted, and the solution was quite simple and strightforward, when you consider the wording provided.

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