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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May 27, 2011 at 5:37 am |
First one took about 30 Seconds. Can’t work out the second one
May 27, 2011 at 5:45 am |
1.) In 2 mins.
2.) No idea
May 27, 2011 at 6:00 am |
Got 1 straight away. Haven’t got time to sit and ponder 2. Can also add just one line to make the equation correct.
May 27, 2011 at 6:05 am |
I can make it a mathematically correct statement with one line.
–Dave
May 27, 2011 at 6:13 am
Me too, but my solution “≠” to that variant isn’t very exciting.
May 27, 2011 at 8:00 am
My first thought too.
May 27, 2011 at 9:42 am
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.
May 27, 2011 at 6:16 am |
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…
May 27, 2011 at 6:23 am |
(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
May 27, 2011 at 6:59 am
… Hmm, national education differences will make (2) rather hard to solve for many people, or at least hard to complete.
May 27, 2011 at 6:25 am |
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.
May 27, 2011 at 6:37 am |
1) 20 sec
2) 3 min
May 27, 2011 at 7:15 am |
I can do it with just one line. And I won’t listen to anyone who tells me my value of N is incorrect.
May 27, 2011 at 7:16 am |
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.
May 27, 2011 at 7:18 am |
Got the first one almost immediately, second one I’m still thinking of!
May 27, 2011 at 7:20 am |
1, 30sec
2, No idea, Sorry ~
May 27, 2011 at 7:29 am |
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.
May 27, 2011 at 7:33 am |
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.
May 27, 2011 at 7:36 am |
I’ve come up with about 6 different answers now. =/
May 27, 2011 at 7:39 am |
Anyway, think I have the solution to pt 1; 2, we will see.
May 27, 2011 at 7:52 am |
i) about 5 secs
ii) about 5 minutes
There is also a 2 added line solution which is accurate to 5 decimal places
May 27, 2011 at 7:57 am |
#1: 3 min.
#2: 30 sec. Also this one has many variants.
May 27, 2011 at 7:59 am |
First is easy. Going to have to think about the second.
May 27, 2011 at 8:29 am |
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.
May 27, 2011 at 9:47 am
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.
May 27, 2011 at 8:42 pm
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.
May 27, 2011 at 9:09 am |
#1: 30 sec.
#2: working on it…
May 27, 2011 at 9:39 am |
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 +-/*.
May 27, 2011 at 9:55 am
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.
May 27, 2011 at 9:43 am |
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.
May 27, 2011 at 9:56 am
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.
May 27, 2011 at 9:59 am |
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.
May 27, 2011 at 10:05 am |
#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.
May 27, 2011 at 10:09 am |
I added four lines to 1) and got a limerick.
May 27, 2011 at 12:05 pm |
Can do it in 1 line (less than a minute) and 4 lines. The three lines with decimal places has got me stumped.
May 27, 2011 at 12:06 pm
Well, I have an answer for 3 lines, but it’s as trivial as my 1 line answer.
May 27, 2011 at 12:14 pm |
#1 – No clue
#2 – About 5 seconds
May 27, 2011 at 12:38 pm |
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.
May 27, 2011 at 12:50 pm |
I did it! I did it! Both of them. I almost gave upt oo.
1 – 30 seconds
2 – 5 minutes.
Really liked this one.
May 27, 2011 at 12:56 pm |
1) 1 min
2) Thought I had it in 5 mins, but only correct to 1 decimal place. Time to reboot head.
May 27, 2011 at 1:00 pm |
OK, I can do part 2 in 4 strokes… struggling to work out how you can do it in 3!
May 27, 2011 at 1:22 pm |
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.
May 27, 2011 at 1:40 pm |
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.
May 27, 2011 at 1:45 pm |
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.
May 27, 2011 at 1:54 pm |
#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.
May 27, 2011 at 2:34 pm
Or does “correct to six decimal places” mean the formula that results in 9.1234562?
May 27, 2011 at 2:15 pm |
first one in 5 secs
second one still thinking and I guess I need the whole weekend!
May 27, 2011 at 2:27 pm |
1. 10s
2. 1min
First idea with any number of lines in 1 sec, but it wouldn’t be probably accepted.
May 27, 2011 at 2:31 pm |
Got the first part in under a minute. The second part is taking me longer. I am not sure what it means.
May 27, 2011 at 2:51 pm |
Got it (part b). I remember seeing this trick in Martin Gardner’s “Scientific American” column over fifty years ago!
May 27, 2011 at 2:55 pm |
Sorry, I meant part 2 not part b.
May 27, 2011 at 4:05 pm |
I can’t answer the two questions, but I can add one line to make the equation correct.
May 27, 2011 at 7:36 pm
If you add one line to make the = into an ≠, it’s not an equation anymore.
May 28, 2011 at 11:02 pm
I can do it with 1 line as well, and keeping the =
May 27, 2011 at 5:25 pm |
Done part 2 in 4 lines. There must be something I am missing, I need the answer before I go bonkers
May 27, 2011 at 6:23 pm |
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.
May 27, 2011 at 7:34 pm |
1. One minute or so
2. Don’t think I quite understand it
May 27, 2011 at 9:30 pm |
No way, I got the first one. About 4 mins. Time to try the second.
May 27, 2011 at 9:36 pm |
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.
May 27, 2011 at 10:10 pm
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.
May 27, 2011 at 10:17 pm
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.
May 27, 2011 at 10:29 pm
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.
May 27, 2011 at 10:18 pm |
Chuffed I got it. Took over 30mins with a pen, paper and a calculator though.
May 27, 2011 at 11:03 pm |
1. 5 sec
2. Didn’t quite get the question. Does this involve some higher math symbols?
May 27, 2011 at 11:21 pm |
oh very sneaky on the notation (part 2), but three lines gets me six decimal places and no more. Classic
May 27, 2011 at 11:23 pm |
I can do it with three lines.
May 28, 2011 at 3:13 am |
can lines be interpreted as commentary sentences?
May 28, 2011 at 6:40 am |
According to one definition in a dictionary, a line is a thin, continuous mark, which opens up a whole new set of answers.
May 28, 2011 at 6:20 pm |
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.
May 28, 2011 at 10:58 pm |
Finally cracked pt 2 I think.. took long enough!
May 28, 2011 at 10:58 pm
Although I think it is correct to 8dp…
May 28, 2011 at 11:00 pm
No, I’m wrong, it is to exactly 6!
May 30, 2011 at 2:47 am |
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.
May 30, 2011 at 6:22 am |
I do not understand the solution for no. 2.. can anyone explain it to me, please?