The following equation is obviously wrong:

but….

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

and

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.

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First one took about 30 Seconds. Can’t work out the second one

1.) In 2 mins.

2.) No idea

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

I can make it a mathematically correct statement with one line.

–Dave

Me too, but my solution “≠”

to that variantisn’t very exciting.My first thought too.

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.

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…

(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,

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

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.

1) 20 sec

2) 3 min

I can do it with just one line. And I won’t listen to anyone who tells me my value of N is incorrect.

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.

Got the first one almost immediately, second one I’m still thinking of!

1, 30sec

2, No idea, Sorry ~

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.

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.

pls i ddnt get any of what u said n i dnt know de answers to any of them…pls help me out

I’ve come up with about 6 different answers now. =/

Anyway, think I have the solution to pt 1; 2, we will see.

i) about 5 secs

ii) about 5 minutes

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

#1: 3 min.

#2: 30 sec. Also this one has many variants.

First is easy. Going to have to think about the second.

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.

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.

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.

#1: 30 sec.

#2: working on it…

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 +-/*.

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.

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.

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.

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.

#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.

I added four lines to 1) and got a limerick.

Can do it in 1 line (less than a minute) and 4 lines. The three lines with decimal places has got me stumped.

Well, I have an answer for 3 lines, but it’s as trivial as my 1 line answer.

#1 – No clue

#2 – About 5 seconds

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.

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

1 – 30 seconds

2 – 5 minutes.

Really liked this one.

1) 1 min

2) Thought I had it in 5 mins, but only correct to 1 decimal place. Time to reboot head.

OK, I can do part 2 in 4 strokes… struggling to work out how you can do it in 3!

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.

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.

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.

#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.

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

first one in 5 secs

second one still thinking and I guess I need the whole weekend!

1. 10s

2. 1min

First idea with any number of lines in 1 sec, but it wouldn’t be probably accepted.

Got the first part in under a minute. The second part is taking me longer. I am not sure what it means.

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

Sorry, I meant part 2 not part b.

I can’t answer the two questions, but I can add one line to make the equation correct.

If you add one line to make the = into an ≠, it’s not an equation anymore.

I can do it with 1 line as well, and keeping the =

Done part 2 in 4 lines. There must be something I am missing, I need the answer before I go bonkers

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.

1. One minute or so

2. Don’t think I quite understand it

No way, I got the first one. About 4 mins. Time to try the second.

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.

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.

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.

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.

Chuffed I got it. Took over 30mins with a pen, paper and a calculator though.

1. 5 sec

2. Didn’t quite get the question. Does this involve some higher math symbols?

oh very sneaky on the notation (part 2), but three lines gets me six decimal places and no more. Classic

I can do it with three lines.

can lines be interpreted as commentary sentences?

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

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.

Finally cracked pt 2 I think.. took long enough!

Although I think it is correct to 8dp…

No, I’m wrong, it is to exactly 6!

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.

I do not understand the solution for no. 2.. can anyone explain it to me, please?