Yes, clearly the operatve word is “if”.(I applaud Giles for describing the math in a way that is easy to get one’s head around) I take issue with several of the above posts that seem to imply that hypotheticals or pure math have no place in the “real world” You can’t get to moon by flying there first to see how much fuel you’ll need.And if one were to take every possible variable into account, then you might as well say that this question is unanswerable because maybe the guy who was supposed to be counting the eggs was actually behind the barn smoking pot and lied about the numbers. lol.
OK, let’s say the problem is “If two plus two equals three, what does two times two equal?” The most obvious answer is that two times two must be equal to two plus two, so the answer must be three. This answer assumes that the only difference in between the hypothesized mathematical system and the standard one is that two plus two is equal to three. However, such a hypothetical system is logically inconsistent. Thus, we must try to figure out how the hypothesis “Two plus Two equals three” can makes sense. There are countless ways to do this, and no two interpretations will necessarily give the same answer.
Thus, when approaching the chicken problem, we have to first determine what the hypothesis means. The riddle is generally taken as a straight math problem, but if you take the stance that part of the hypothesis is that chickens don’t work in halves and egg halves never get laid by themselves, you get a different answer.
landroid said:
Thanks, landroid, I should have thought of that.
glowacks, that is not the same situation at all. Mathematics has an inherent structure that can’t just be assumed different by changing one detail. You have either redefined what “two” means, or you have redefined what “plus” means, or you have redefined what “three” means, or you have redefined what “equals” means. So that proposed problem is unclear because it does not explain what is different.
Assuming that a unicorn exists and has one horn, however, is a simple assertion with no effects to the rest of the computation. Similarly, for one to think about half a chicken doing anything, one only needs to assume we’re talking about average rates. Same way the average family size in America is 2.5 children. That does not assume anyone has half a child.
Yes, “one only needs to assume”. But what if you think that such an assumption is wrong? What if there’s a different set of assumptions that make sense? My contrary-to-fact mathematical hypothesis is certainly much different, but demonstrates it in a situation where you have absolutely no idea what the hypothesis means. And there’s been three different interpretations of the chicken problem, none of which is any more or less reasonable than the other for the sake of determining what the hypothesis means.
“The average family size” says it’s an average. “One and a half chickens lay one and a half eggs” does not mention averages and thus it is reasonable to assume that the situation posits actual chickens with this behavior.
And by “reasonable” I guess I really mean “consistent”. That is, there’s no way to argue the interpretation is wrong by showing an internal contradiction - you have to argue another interpretation is “more” valid.
Also keep in mind if you start the timer just before a chicken lays an egg as opposed to just after you are cutting it down from six days to under five, assuming they lay them periodically at a fixed interval.
If we posit it as “if 15 chickens can lay 15 eggs in 1.5 days, how many chickens to get 60 eggs in 6 days?” then can we see more clearly?
Number 43, you are a genius! Calls to mind the “millenium controversy”: Was Year #1 the first year of Jesus’s life (assuming he existed, yadda, yadda) or was it the year that we typically describe a child as being one year old?
Except nobody ever said anything about half-eggs getting laid by themselves.
Consider a hypothetical but plausible example: My mom has three chickens in a coop, in three nests arranged on an east-west line. Each chicken lays one egg every 36 hours. How many chickens does Mom have in the west half of her chicken coop? She has one chicken entirely on the west side, and another sitting on the middle line. So she has a chicken and a half on the west half of her coop. And how many eggs do those one and a half chickens lay, in the west half of her coop? The one on the end lays an egg every day and a half that’s entirely in the west half of the coop, and the one in the middle lays an egg on the line, that’s half in the western part of the coop. So in the west half of her chicken coop, my mom has a hen and a half laying an egg and a half in a day and a half.
glowacks said:
There’s nothing difficult about the problem as stated. You are only being obstinate to seem smarter than the rest of us by positing that the logic is flawed because it talks about half chickens and half eggs. If you want to get your jollies being smarter than the “sheeple”, go for it, just don’t expect me to go along for the ride.
Irishman
The original puzzle posed is of a kind used by the mathematically minded to fool those who are less educated. Invariably many ordinary people get the answers wrong. That allows the maths/logic geek to poke fun at them by showing the “correct” answer.
As you can see from the replies above, maths/logic geeks lose their minds if you indicate that their superiority may be less clear.
Glowacks and I know what the “correct” answer is meant to be. We understand the conventions of mathematical and logic puzzles. However, we are pointing out that the question uses real objects to set out its puzzle. Those real objects have a real nature, which the puzzler wants us to disregard.
However, he does not tell us to disregard reality. If the puzzler is so lazy, that means the puzzle has multiple rational solutions. Not a single solution which the elite can wave at the uniniated.
IANA ‘maths/logic geek’. I could change my username to SucksAtMath.
But this isn’t a ‘puzzle’ at all. It’s just a ‘word problem’ like you’d get in elementary algebra. No ‘assumptions’ have to be made, even if you refer to ‘real objects’. Obviously half a chicken can’t lay an egg. Obviously, a chicken can’t lay half an egg. Therefore there is no other interpretation of the problem other than that someone is using a number of chickens that lay a number of eggs at a given rate, and the average number of chickens and eggs is one-half. See? No ‘puzzle’.
But repetition of ‘and a half’ sound funny when you say it. Maybe the Marx Brothers used it because it sounded funny. But there’s nothing in the problem that doesn’t make sense.
The real puzzle is why Marilyn vos Savant, who is supposedly ultra smart, thought that " If a hen and a half can lay an egg and a half [in a day and a half], that means a hen can lay an egg in a day."
No it doesn’t, as Cecil says. It means a hen can lay an egg in a day and a half. She may be smart but she sucks at maths.
Who said anything about “rate”? OBVIOUSLY the answer is 6. There is no indication that more eggs will be laid the next 1.5 days. The point is that its silly to question one assumption without questioning them all. (Next we can debate “half” of a day. What’s THAT?.. nature of time, reletivity, “days” last 6 months in the arctic, yadda, yadda) The answer “xyz, because half a chicken can’t lay eggs” is not an answer, its a punch line, which makes the question a joke, not a puzzle. Of course, no one SAID it was a puzzle. lol
Michael of Lucan
So you agree you’re just being obstinate.
The same could be said about puzzles of every kind. It is inherent in the nature of a puzzle - someone wants to see if you can figure out what they know. Do you hate all puzzles and quizzes, or only math and logic ones? Are crossword puzzle creators poking fun at all those people who don’t know what a three letter word for valley is? (Hint: it’s discussed in the thread on vowels.)
This puzzle is not especially difficult or confusing. The only trick to it is that it deals with all the halves, so one has to pay attention not to get lost. The standard quick answer is assume all the halves cancel out (like Marilyn did), but the fact is there are 3 halves, so only 2 cancel.
Now if you want to make a trick question, look at this puzzle:
If a chicken and half can lay an egg and a half in a day in a half, how many eggs can 6 chickens lay in 6 hours?
Answer: six 1/6ths of an egg, NOT 1 egg. It takes a chicken a day and half to lay an egg, that can’t be sped up by increasing the number of chickens.
It’s like the old joke, if it takes one woman 9 months to have a baby, you can’t get the job done sooner by hiring more women.
See how the first one is a math problem, the second one is a mean joke?
That’s what you’re doing - taking a math problem and turning it into a mean joke. And you’re saying that it’s the math/logic puzzle lovers who are the mean ones.
Hens can lay half eggs. Not half the shell and a gap on the other side, but half the volume. (The shell is half by weight not area).
These are called new eggs, and like new potatoes are small and tasty. If fertilized they will produce full size chicks, just preemies.
Though not sold in most stores, if you go to the chicken ranch you can buy them by the 2-dozen.
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Bravo Brainiac! That the “half” chicken was a runt was an idea that had occured to me also when I was thinking about how to explain away the “logical inconsistancies” (as one poster put it) and still arrive at the “right” answer.