John is a gardener. The other day he bought a stack of posts and decided to put them around his garden. He planted the posts 2 feet apart and found that he needed 200 extra posts. Annoyed, he pulled up his posts and replaced them, but this time placing them 3 feet apart. Now he had 25 posts over. How many posts did he buy?

As ever, please do NOT post your answers, but do feel free to say whether you think you solved it and how long it took. Solution on Monday.

If you enjoy the Friday Puzzle, remember that I have produced a kindle ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available in the UK here and USA here.

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Ah, a good old fashioned maths puzzle. Felt like I was back in 8th grade!

I got confused at the start but I’ve got it now.

Sovled. took 1 minute. But, if I should consider the thickness of the posts….

Usually when saying “placing them -x- apart”, it means from the heart of the post to the haart of the next post. So thickness is not relevant.

There is something else that is relevant: Is the garden completely around the house, or is there an extra 2 or 3 feet after the end of the last post? That gives me two possible answers.

Seemed pretty simple. When/where is the answer posted?

“Solution on Monday.”

“posted” chortle see what you did there.

I think I got it but I disregarded the thickness of posts, i.e. assumed the distances were from measured from the center of the posts.

Hooray for maths. Number of posts and circumference of garden found very quickly.

Gareth,

Do you mean “circumference” or “perimeter”?

The answer is: “not enough”. 🙂

Nice one!

Not enough for a 2 foot distance—

Too much for a 3 foot distance…

Which distance would he have selected for all Post he already had…

easy one this week. ~2 min to find the answer

Hooray for algebra. 1 minute. Unlike last week when I was completely tricked.

the solution to this problem of course is to measure your garden before planting the posts.

Trial and error – 1 minute. I just used numbers – ignore the fact they were “real” posts LOL

Hooray for algebra indeed. About a minute.

M’s right. It’s unclear if there are posts in each precise corner of the yard or if there is a 2 or 3 foot space around the edges (like what “padding” means in CSS).

I assumed the former and got into quadratic equation hell very quickly.

The missing puzzle information, to make it dead easy, is probably that the area of the garden = the number of posts needed to fill it.

I think you’re going down the wrong track. He’s putting posts ‘around’ the garden – i.e. circumference. No quadratics needed, if I’m right.

Good grief, the English language is ambiguous. The word “perimeter” would’ve helped.

I guess I was just hoping the problem was more complex than a simple ratio.

Don’t forget the duck moat as well, no posts needed for that.

Done. Simples. I did this while ‘ simultaneously’ eating breakfast.

Thought I’d do things properly for a change and worked out an equation, which gave me two incorrect answers – c. 5 minutes. Gave up on doing things properly, used trial and error, found one answer that works – another 5 minutes.

just realised where I went wrong with my equation. The equation itself was fine, it’s my Maths that was rubbish.

Simple.

About a minute to a wrong answer (foolishly got a sign wrong in my calculations) After a quick check of the answer shows it wrong, wrote it out properly and got the right answer (assuming the fence joins up to itself, and isn’t from, say, a house wall to a house wall).

I had some trouble with this one. Figuring out that “replaced” did not mean “thow away and buy new ones” but simply “putting them in other spots” was the hard part. About 10 min in total I guess.

John bought all of the posts.

Couple of minutes with a couple of variables

My head hurts- I will have to sit down with a pencil and paper to work this one out. I knew this would happen after I got last weeks really quickly!!

Only took a few seconds using simultaneous equations to find the number of posts and then the length of what he was trying to cover. To begin with I was contemplating the shape of the garden but that turns out to be not useful at all. Just had to remember that 2 posts cover 2 feet, and 3 posts cover 4 feet etc.

Apparently simple maths, but the real problem relates to the fact that John’s CEO is unimpressed by his ignoring forward cash flow projections. Budget limitations have been forgotten and actuarial assessment of future required post numbers and thus expenses have serious implications for imminent IPO of garden.

John sacked, post cost is hidden under “miscellaneous” and actuary takes 3x cost of posts in consultant’s fees.

I must have got it wrong, because it was TOO easy.

I don’t think I can solve this. I have some ideas, but this one’s too mathematical for me. Divided by 1/8 and then multiplied…:-) This one is solved by Pythagorean problem..I guess? Something must be done to 175..

I think I have the answer. I took about 10 mins. I actually have two answers, depending on what kind of puzzle you decide it is; although I am pretty sure which answer you are chasing is my second answer. I look forward to seeing the correct answer and the logic.

Thanks,

Phil.

I set up a quick system of equations and I got it in about 5 minutes. I’ll look forward to the answer on Monday to see if I’m right.

Got it within a few minutes with the help of a trusty pencil and piece of paper!

One minute.

About 10 seconds with WolframAlpha

Think I got it using algebra as it all works out nicely with 1 gotcha in the way fence posts cover distance, but I’m worried now after reading a comment there might be another gotcha (which undoes the first one) when they form a loop which makes a difference of 1 in the answer…

Saw how to tackle this straight away, about a minute to do the algebra, a minute to check the answer, and another minute to re-do it in case the gotchas cancel out

About 7 minutes to find the simpler answer (2 or 3 ft apart meaning from the center of a post to the nearest one – not enough information to solve it if the distance is from a post’s border to the other – and assuming the posts are placed over straight lines).

I’m being lazy with the last assumption: from the puzzle formulation, we discover that the work could have be done with N+200 or with N-25, in other words, with an odd or an even number. The natural way of doing it would be to put posts in the vertex of the perimeter… but that excludes the rectangle as the figure for the garden. Interesting how this raises the extra puzzle of knowing the shape of the garden. If I don’t put posts at the vertex, the puzzle became a lot more complicates and maybe not deterministic.

Shapes are not a trivial thing in this puzzle. Take another natural shape to choose, the circumference. The funny thing about the circumference is that if we sum all the distances between consecutive posts when we have distance between them of 2 or 3 ft, assuming there was enough posts in each case, the results are going to be different for each case, although the perimeter is the same.

Yes, the result will be different because in one case he doesn’t make it all the way around the garden, and in the other case he makes it all the way around and has posts to spare.

Not because of that but because distances are taken in a straight line, which will not coincide with the line of the circumference. To present an extreme example, lets say I do the job with 4 posts, spaced by 30ft between each pair. How much spaced they should be if I use only 3 posts instead? First reaction would be to say, 40ft, but that would fail for a lot of shapes or configurations. For a circle, for example, it would be ~36.7ft, if I’m not wrong.

Couple of minutes with pen and paper.

Well, that was a nice gentle one. About a minute, including jotting down notes in Metapad (a much friendlier freeware text editor than Windows Notepad).

Assuming the solution is just simple algebra, it only took a few seconds to solve—then a few minutes to try to figure out if there were any tricks because it seemed a little too easy.

Come on! Too easy! This is just 5th grade math!

Why didn’t he measure up before buying his materials?

My maths are so rusty that my first answer was a negative number, two minutes of concentration got me a proper answer.

Either I’m way wrong or 15 seconds.

The puzzle for me is why can’t I just count the damned things? I mean… really! People living in PuzzleLand are weird. They’d rather get by with limited information and go circuitous routes to the answer than just do the easy thing to get the same information in less time and less effort. Crazy!

What would the fun be in doing it the easy way? First you have top put some absurd restrictions on yourself, THEN do it the easy way. 🙂

Goodness me I’m rubbish at maths haha! Still trying!

It took about a minute, maybe 90 seconds, mostly because this sort of problem was what we had to do all the time in 4th grade, so I’m used to it

I love the way some people always try to make the puzzle more complex than it actually is. Simple highschool algebra this one, with no tricks.

Clearly John is not a very good gardener or be would have sat down and done the math before starting the job.

He will probably forget to put an opening in the fence too.

But this also begs for a follow-up question. How many new holes did John have to dig after changing the distance between the posts?

Easy math about 2 mins because of lack of pen and paper

I think I got it – waiting til monday to find out!

Got it, took around 5 minutes, most of the time spent finding the right equation.

About one or two minutes. I could see what equation to set up, but used pencil and paper to solve it.

Try putting the posts 3 3/13 feet apart.

Been working on it for 20 min or so not getting anywhere, I always get the math ones, don’t know what’s wrong. Just to clarify- he would have required 200 extra posts but did not buy them, right? Just used the ones he had , but spaced them 3ft apart instead and had 75 left over. I’ll be so embarassed when i finally get it

Terrifying now i’ll in no way obtain 1 yet again