I want to promote this site offline by printing one of the problems found here on a business-sized card to be distributed somehow in the real world.

I'd like to ask people's opinion on which problem this should be.

There are a few requirements: it has to be fairly easy to solve (definitely without using any heavy duty math), but still give one a sense of satisfaction having solved it. It has to be relatively short, to match the attention span of whoever picks up the card, also to fit on the card in the first place in a font that's big enough to be readable. It should be interesting enough that a person who's not neccessarily a puzzles fan, would still be interested in giving it a couple of minutes' thought - and may even tell a friend or two. Well, you get the point.

Looking at the problems currently listed as top rated, you will notice that most of them do not fit these criteria very well, so I wanted to ask the visitors here what their opinion was on the matter.

Please "nominate" any problem you wish here (provide a link to make it easier to find), and we'll see if maybe we can come up with something to draw in the crowds.

I'd propose an additional requirement that the puzzle not be too well known.

It's not a very highly rated one, but I'd say "The party" is a pretty good representation.

Selected problems (at most 3) from the 'Knights and Liars' category might also help.

Drew and Mohammad come back.

Probably for your criteria, the 'Brothers and Sisters' one is the best for your criteria. :) I think Yes sir! would be good, but many might not get that.

Here are a few problem which I would suggest from the other categories:

A Pack of Prudent Pirates submitted by Levik (Logic)
Mutually Friendly submitted by Levik (Logic)
Ties submitted by Half-Mad (Logic)
The Four Mathematicians submitted by Ravi Raja (Logic)
Mr. and Mrs. Brown submitted by Levik (Logic)
The Three sages submitted by Levik (Logic)
Light bulb submitted by Half-Mad
The Three Logicians submitted by Ravi Raja (Logic)
An arrangement of 15 submitted by Levik (Numbers)
Self-Descriptor submitted by Levik (Numbers)
Self-Descriptor part2 submitted by Happy (Numbers)
The Ten Statements submitted by Ravi Raja (Logic)
Two numbers submitted by Happy (Numbers)
Fathers and Sons submitted by Ravi Raja (Logic)
Unknown Answers submitted by Tim Axoy (Knights and Liars)
Four-Digit Number submitted by Ravi Raja (Just Math)

Personally, I'm not a big fan of paradoxes. I haven't seen one yet where the self-contradiction wasn't easy to spot, and there's not much to do once you've spotted it. They're not very satisfying because you don't get any closure from an actual solution - all you're left with is some logically inconsistent statements.

Well seeing as how your making business cards i'm assuming this would be a rather small project (The making of the card that is) so that the same card could be made but with two different puzzles. I think 1 should have a riddle and 1 should be logic oriented (Including math). This way we would appeal to both groups of puzzle people. Riddle lovers and math lovers. Anyways 2 problems i highly recommend. 1. String around the cylinder. 2. 2 colors

my 3 cents worth.
Basing on the need for shortness (to fit on a card) appropriate difficulty(not so hard to scare people away if no answer is included(which it shouldnt be) and not too easy that people will dismiss it), I'd like to second the choices of "2 colors" and "the party". Certainly though, there are lots of good choices.

What I really love about "The Party" is that the solution is VERY satisfying, much like unraveling a good mystery.

However, I fear that 90% of the people would not come up with it. Maybe I'm wrong though.

(Please don't mind my being picky - it's just that if I will end up plopping down 100-200 dollars for business card printing, I would like for the content to be as good as it can).

All you can do is ask. I solved the party, but couldn't get burning ropes (going on memory that burning ropes was trying to time 45 minutes with 2 ropes), so either I'm the abnormality (likely unfortunately) or burning ropes is harder than you realize (its a simple enough concept, but definitely not something I'd have thought of).

On a side note, how does a guy survive in NYC when a mere set of business cards cost that much? You can probably get yourself a self-making card program for much less than that. My company has one, as I'm sure many others do. On top of that, outsourcing business cards here costs about $15-$25 (CDN) per 1000 cards, so I have to admit that I'm awfully shocked.

Yes burning ropes is one of the most genius puzzles i've ever heard in my life. I'm all for burning ropes.

Alan, I responded in a comment attached to the problem, so as not to give away the solution in here.

I'd vote for Fly on a Cube.

The reason I like "Burning ropes" is that it's viral - there's no way that you can be explained the soluiton and not understand it. "The Party" has a few steps one must take before solving it, and I personally found that some of my friends had trouble following as I explained the solution.

That said, "Fly on cube" is pretty good too (especially so since it has an image) - but the concept involved is basic geometry and may not be as appealing to some people.

As far as printing costs, the price I mentioned is based on twosided full-color cards on glossy stock (I want them to be in flooble blue and with the perplexus logo one side).

I'm sure I could get plain old black on white cards significantly cheaper.

I think Burning Ropes is a good puzzle :) I thought it was a cool idea when I saw it, as I would never have thought of that!

I'm a bit late coming to this thread, but I'd like to present an alternative view of the burning ropes puzzle: namely, that the puzzle is flawed, and the solution would not necessarily work. In fact, there is a hidden assumption, without which there is no purely deductive solution.

The problem lies with the assertion that a '1 hour' rope lit at both ends will burn up in 30 minutes. Consider the following rather weird piece of rope.

A->->->->->->C<-<-<-<-<-<-B

Ignite at A, the flame takes 20 minutes to reach C, and a further 40 minutes to reach B.

Ignite at B, the flame takes 20 minutes to reach C, and a further 40 minutes to reach A.

This is consistent with the puzzle statement.

However, if we ignite the rope at A and B simultaneously, the flames meet at C after only 20 minutes!

You may ask why a rope should burn faster in one direction than the other. Strictly speaking, of course, the reason is irrelevant; the puzzle is already broken. But there are plausible reasons for a preferential burn direction. Perhaps the rope is resting on a mound, so that it is easier for a flame to progress upward than downward.

Or maybe the ends of the \">" and "<" symbols, in the diagram above, represent frayed strands of rope, preferentially sticking out to the left on the left hand side of the rope, and to the right on the right hand side of the rope. They may allow a flame to progress faster by more easily igniting the frayed strands from one direction.

The bottom line is that there is no purely deductive solution. We need to know something about the physical properties of the rope. That is, unless we add to the puzzle statement the hidden assumption I referred to above. It is this: in each section of rope, the rate of burning is the same in either direction.

It's true there are many possible factors that could influence the validity of the solution. However, this is a *logic* puzzle. When a logic puzzle posits a rope which does not burn at a uniform rate, a *closely related* question is: does it burn at the same rate in both directions? It is also a relevant question, as any solution depends upon the answer. Therefore it seems likely that the poser omitted any mention of directional burn rate either because: a) he/she overlooked it; or b) it would be too big a hint.

Either way, in my opinion, we have a flawed logic puzzle.

Alan, then how do you explain the counter-example rope in my October 7th post, above?

Light either end of this rope and it burns out in 60 minutes. Simultaneously light both ends and it would burn out in 20 minutes.

DJ, on the contrary the assumption that a rope will always burn at the same rate in either direction is in need of justification. Practically, I believe it is quite likely that any given rope will have sections that burn at different rates depending on the direction. Logically, it is possible.

The complete statement of the puzzle premise is: "You have two ropes. You know that each rope takes one hour to burn from one end to the other, but that the burning does not take place at a constant rate (i.e. half the rope may burn in one minute, and the other half will take 59 more minutes to burn)."

It seems to me the second sentence is saying that burning does *not* take place at a constant rate. It then gives a numerical example to reinforce the fact that the first half (by length) of the rope need not burn in 30 minutes. It doesn't imply that each half burns at a constant rate. And it certainly doesn't preclude the possibility that sections of the rope may burn at a different rate in either direction.

What I mean by my first comment is wouldn't the frayed strands no matter what burn in the same length? Even if they ignited, wouldn't the rope still burn at the same rate?

Anyway, I would feel like adding "frayed" strands to the problem is really trying to find SOME way to make the problem wrong. The whole point of the puzzle is to assume that the rope is normal, no frayage, no "different burning in other directions", and no dousing in gasoline half way through. In my opinion, if the rope is just pure rope, it isn't possible to have it burn in another way.

Nick, I believe you are nit picking. The assumption about a rope is that it will burn, do so uniformly and at the same rate in both directions. In our case, the rope does NOT burn uniformly, so we specify that conditions. All the other regular rope "defaults" still apply.

I don't believe anyone would think of the solution and then discard it on the basis of ropes burning at different rates each way, and as such, specifying that they burn the same reguardless of direction is not strictly neccessary. It would however provide a hint that I belive the problem is more interesting without.

levik,

When I first heard this puzzle, maybe five years ago, I was disappointed with the purported solution for the very reason you suppose nobody would be! But I agree that, with the directional assumption, the solution is elegant.

I understand your idea of regular rope "defaults." Were we dealing with a completely regular rope, I could almost agree it would not be necessary to specify that burn rate is independent of direction. But when you introduce a rope where one half might burn 59 times faster than the other half, I'm afraid all bets are off, as far as I'm concerned. Then it is quite legitimate to question the directional burn rate. Indeed, I strongly suspect such a rope *would* have sections that burn faster in one direction.

Here is the basis for an abstract solution that does not assume the burn rate is independent of direction. It requires the use of a knife.

Chop the rope in half and simultaneously ignite both left ends. (Without reorienting either section, of course.) If they both burn out at the same time, we have measured 30 minutes. If not, instantaneously chop the unburnt portion of rope in half and ignite the non-burning left end. And so on, ad infinitum...

Since, at any given time, we have two pieces of rope burning *in the same direction*, once the entire rope burns out, we have measured 30 minutes!

If we treat this as a logic problem, and conceptualise the burning rope as a line segment with point(s) moving along it, this approach offers some advantages over the standard solution. Firstly, as already mentioned, it does not implicitly assume a unidirectional burn rate. This appeals (to me) aesthetically. Secondly, it can immediately be generalised to yield a way of measuring 60/n minutes, where n is a positive integer.

As a solution to a physical problem, it may or may not be more accurate than the standard solution, depending upon the nature of the rope. (You would, of course, chop the rope only a few times.)

Ok nick now i think i understand the rope burning in 40 minute thing but maybe i don't but now here the thing. The question asks "how can u measure out 45 minutes" So If you put the rope in such a way or hold it up in a direction that causes it to burn "improperly" then you simply didn't solve the problem. You are wrong because you didn't solve the problem. the problem is not wrong because you found a way to come up with an incorrect answer. What I'm trying to say is If you do the things you're talkin about that come up with an incorrect solution, well then you're incorrect, plain and simple. hers the solution. Lie both ropes flat down on any surface (Please don't argue abou surfaces now) and light two ends of one rope and one end of the other. Next when one rope burns out light the end of the other rope. the solution does not say put the rope in an inverted v so it burns in 40 minutes now does it say hold the rope in an upward direction causing it to burn un-uniformly.

Alan,

Placing a rope on an inverted V-shape is just one example of how it may burn faster in one direction than the other.

Another possibility is that the rope construction itself could confer a bidirectional burn rate, and over this the puzzler has no control. Whether this takes the form of an asymmetrical construction, or frayed ends, or is a consequence of a very inhomogenous structure (one half of which may burn *59 times* faster than the other), it is a distinct physical possibility, and a definite logical one.

Therefore we cannot reasonably deduce that a '1 hour' rope, lit at both ends, will burn out in 30 minutes.

Ok lets take this one hour rope and work with it ok? first lets take this rope and light one end. According to the rule it should burn out in one hour. Now lets "revive" this rope back to its original state. And light the other end. Note that this time it would also take one hour to burn in order to up hold the rule of it being a one hour rope. if the rope burns "faster" in one direction then there fore it is no longer a one hour rope, and using that rope would not constitute it as a part of any solution to that problem. As we can see the the problem clearly states "If one end of the rope is lit then the rope will burn out in one hour" the existence of this statement prevents the rope from taking more than one hour to burn in either direction. Now that we see every rope burns one hour both ways we can deduce that one both ends are lighted it will take half an hour to burn. And with simple logic we see the rest of the solution that is on flooble right now is correct.

But it is a normal rope other than that aspect! When you don't see anything to the contrary, you are to assume it burns like a normal rope. The only thing you see is that it doesn't burn evenly across. The other stuff you have to assume is even unless otherwise satement. And one thing different isn't that wierd is it? Haven't you found many other things to do to the rope to make it burn in all sorts of obscure fashions?

OK... I am not as perceptive... I am rather closed minded and would never think of frayed edges or different rope postions so it is good for me. :)

I think its an interesting puzzle, and helps remind us to be more specific in our wording. :)