A Brainteaser

I'd think it's that "any five" that could be tricky. There could be some that individually had less than 1/5 of a cig worth of tobacco, but taken with others with more could achieve that 1 cig average. Right off hand though it would seem like one could get at least 5 cigarettes from the sets.

6

they make 5 cigarettes then smoke them and have enough for a 6th and then enough for a 1/5 of a fag

any real smoker would get it

p

Sadly, I did this a lot in my younger years. Hospitals were the best source for half-smoked cigs. You have to be very desperate to roll one from leftovers though. Tasted absolutely horrible.

That being said, I'm probably over-analyzing this, but the question assumes one cigarette equates to a particular amount of tobacco. When rolling your own, the variables involved (preference, paper being used, tobacco being used) can cause that amount to vary wildly.

This is why I'm really bad with story-questions. I read nuance where none is intended.

I think you need to add something to let the non-smoker reader know what the Peak Oil Poet knows, that cigarette butts are normally extinguished at a stage where they still contain this amount of unburnt tobacco. I didn't know that a typical butt would have this property.

If the smokers know that tobacco is in short supply, why don't they smoke all the tobacco in the cigarette rather than extinguishing it with unburnt tobacco still in it? Is it not possible to smoke all the tobacco in a cigarette??

There is an ambiguity about the "one" cigarette they can make. Is it exactly one, or at least one, or one with a bit over (ie between one and two). Suppose there are four butts that are almost empty and 21 that are basically whole cigarettes. Does that satisy the conditions?

The "any five butts" descriptor is vague. There are two possible meanings. The first is that each butt is the same size, containing one fifth the tobacco of a full cigarette. The second is that the amount of tobacco is variable, but that the five smallest butts have at least 1/5th of a full cigarette's tobacco.

In both cases, the only valid answer is "at least five".

Under the first interpretation, turning the five newly created cigarette butts into a sixth cigarette is not guaranteed to be possible, as it cannot be assumed that all cigarettes are extinguished after consuming only four fifths of the tobacco.

Under the second interpretation, the answer can be as high as 300, if one assumes only that the label "butt" applies to a cigarette which has had some tobacco consumed. The first round could have 24 cigarettes, the second 23, the third 22, and so on down to 1.

You have to unambiguously establish that 20% of the original tobacco always remains after a cigarette is smoked (without giving anything away) to get an answer of six, assuming that's what you were aiming for.

I'm sure this has nothing to do with anything, but I did find it a little curious that the first two sentences consist of the "narrator" telling us facts directly, while the third sentence instead tells us what "the smokers know" instead of telling us directly the thing that the smokers know. Why is the point of view of the smokers suddenly something that comes up in the third sentence?

From every five bus they can recover enough tobacco to make a cigarette, but it takes more than just tobacco to make a cigarette. What about papers?

I assume the answer you want is that they can make 5 cigarettes out of the 25 butts that they start with, smoke the 5 cigarettes, leaving 5 more butts which they can use to make 1 more, for a total of 6 cigarettes.

The statement of the problem seems to me to be fine. A puzzle like this, to be a good puzzle, needs a bit of ambiguity, a "twist". Here the "twist" is the 6th cigarette made from the 5 butts remaining from smoking the first 5 cigarettes made from the 25 original butts. If the puzzle were rewritten to make it clearer that the 5 remaining butts were to be used to make an additional cigarette, then it would effectively destroy the puzzle as a puzzle. These puzzles require, once the answer is revealed, thep possibility of a "oh, of course; I didn't think of that" moment which too much clarity destroys.

You need to clarify whether or not the group of smokers is cyclic. ?

Nice to see that setting good problems is as difficult here as it is in genetics. (I have a genetics MOOC and the students seem to spend most of their brainpower pointing out ambiguities in the problems I set them.)

As written, the answer is "at least 25". There is nothing to imply that the 25 cigarettes would be smoked. A 26th cigarette would require an action not specified in the set up, and would not be made from "...the available butts."

Let's get metaphysical.

I take the first three sentences to say that any five butts, chosen at random from the 25, can be combined to make a new cigarette, and that the smokers plan to make new cigarettes in that manner (rather than, say, pooling all the tobacco from the 25 and making the new ones from the heap).

The last sentence has an exploitable ambiguity: "How many new cigarettes could they make with the available butts?" Well, each cigarette made will have tobacco from five distinct butts, so there are 25!/(20!*5!) = 53,130 distinct new cigarettes they could make. Of course, they will only end up making five of those (and perhaps one later given the right circumstances).

@13 - Gaak! Typos. That's 5 and 6, not 25 and 26.

I suppose one "wording" problem would be: What constitutes a "new cigarette"? Exact full size of the originals? Without such definition one could argue that mixing any amount of usable tobacco from one butt with another creates a "new" cigarette of unspecified size.

The statement that smokers knew that material from any five would make a "new" one does not rule out, say, any 4 making the newbie. That is, without the previously mentioned definition.

Being more of a butt than a new one myself, I'm sure I'm missing something so I will console myself listening to the Kinks song "Harry Rag" from the oh-so-wonderful album "Something Else":
https://www.youtube.com/watch?v=SPN81cFRX5M

To put it more clearly, and with the numbers right, if you want the trick answer of 6, the question needs to read along the lines of "how many cigarettes can they roll and smoke from the 25 butts". As originally stated the answer is 5, because that is all you can roll from what's available.

As the problem is stated (any five butts include enough tobacco to make another cigarette) I think you wanted Another Matt's answer: the combinations of 25 things taken five at a time. Otherwise the wording is too ambiguous to determine an answer. Which is to say, overall the statement is quite ambiguous, but there is one way to interpret it which gives a definite answer, without having to make any assumptions about smoker behavior and so on . So it could be a brain-teaser on a meta-level. It could be made easier by adding something like:" The answer is a specific integer, with no additional assumptions required.)"

And after submitting my comment, then turning off my laptop to watch NFL football, I realize the problem statement is still too ambiguous. How do we know that there aren't four butts with enough tobacco to make another cigarette?

I think Bill #16 makes a valid point. I'm reminded of the old "if it takes a man a day to dig a hole how long does it take him to dig half a hole" chestnut. (Answer: there's no such thing as half a hole, dumbass!)

Is there such a thing as "half a cigarette"? Or is that just "a small cigarette"?

So, Jason,

Is there something specific you were getting at with this? I'm disappointed there was no followup post!

Bit late, I know, but I agree with Bill. The ambiguity is in the phrase "any five butts contained enough tobacco to make one new cigarette." Since it says "any five" and since we can probably assume the butts are not all the same size, then the five smallest butts will make one new cigarette. It may be that the next four smallest will make one new cigarette then the next three smallest and so on.

So it is actually an unanswerable question. And, of course, as the Peak Oil Poet notes, smoking whatever number of new cigarettes are rolled is not the end of the rolling....