Chicken and a half.

Reference to this Column:

http://www.straightdope.com/columns/read/915/if-a-chicken-and-a-half-can-lay-an-egg-and-a-half-in-a-day-and-a-half-how-many-hens-to-lay-six-eggs-in-six-days

The answer is clearly two hens, but it seems as though you passively dismiss it with an attempt at sarcasm by stating “no excuses about how half a hen can’t lay anything–we’re talking science here.”

The fact that half a hen cannot lay an egg is incredibly relevant. Why would you proffer 1.5 hens as a solution in the face of such a glaring logical inconsistency?

You’re kidding.

No, actually Cecil’s kidding: you just didn’t get it.

Marilyn was correct, however bad her logic. As indicated, half a chicken tastes good (ideally it should be cooked first). However, we know it cannot lay eggs.

So, we are told the chicken and a half can lay at a rate of 1.5 eggs per 1.5 days. That means one chicken, doing all the work, lays at a rate of 1.5 eggs per 1.5 days. The half chicken just lays there.

Therefore that one busy chicken lays six egss in six days.

Seems obvious to me. The answer is one.

This isn’t reality, it’s a math logic problem. Cecil has accurately done the math.

If it makes you feel better, multiply the whole problem by 2.

“If three hens can lay three eggs in three days, how many hens does it take to lay 12 eggs in 12 days?”

Answer:

3 hens = 1 1/2 hens x 2

But the question does not say - “This is a purely mathematical problem, and you should ignore reality in answering it.” It uses explicit terms and refers to real objects.

My answer is factually correct, in dealing with the factors supplied by the question.

The “mathematical” answer you suggest is based on the bad premise that half a chicken is as functional as a whole one. In real life, chickens do not lay eggs when they are chopped in half. They lay dead, not eggs.

Applying good logic to a bad premise results in a wrong answer. And that’s why a lot of intelligent people get nowhere in life. They fail to check their original premises before applying logic and speeding with great intelligence to a dumb answer.

But even live chickens do not lay half eggs. The fact that the egg is divided as well as the chicken is a tip-off that you should treat it as math, not biology.

But twice the number of hens will be able to lay twice the number of eggs in the same amount of time. Three hens will still only need 1.5 days to lay 3 eggs. You have changed the rate of laying.

6/1.5 =4
So, in 6 days three hens will lay 4x3, i.e. 12 eggs. But you only want 6 eggs in 6 days, so halve your number of chickens = 1.5

As that is what Cecil said, it must b right. :cool:

Michael of Lucan

The problem clearly posits a condition: “If”.

The phrasing of the problem statement mentions half chickens and half days. Reality doesn’t work that way, but math does.

The trick is that the halfs are what make the problem confusing. If you multiply by 2 like I did, it becomes a simple math word problem. But with all the half’s thrown it, it gets more complicated.

njtt said:

My point wasn’t to get the same answer, it was to demonstrate the math problem without the halfs. Note that the x2 carries through to the answer.

I disagree with your reasoning but I love your play on words. :slight_smile:

Let’s say I have two hen houses: One house I own 50/50 with another person, and the other house, I own 100% of the whole shooting match. Due to various circumstances, we now only have a single chicken in the first hen house. I own 1/2 of that chicken, and my business partner owns the other 1/2.

To answer that question, I’ll use the 1/2 chicken I own in that first hen house, and a whole chicken in the second hen house. Thus: 1 1/2 chickens!

Yes, this is an accounting fudge, but we do this type of stuff all the time. Can you really have -5 dollars in your bank account? No. You have ZERO dollars in your account, but you owe the bank $5. When you deposit $10, the bank will take $5 out of that to pay itself back.

Let us suppose that this isn’t a strict math problem and is supposed to take into account certain biological requirements. The “half a day” is clearly just 12 hours. A half chicken cannot lay eggs so if one and a half chickens lay a certain number of eggs, then one chicken must have laid them all. The only way a half egg can be laid is if the other half is also laid.

Thus, “one and a half chickens lay one and a half eggs” means “one chicken lays two eggs”. If this is done in 12 hours, then over 72 hours one chicken can lay 12 eggs. Thus, since one cannot have a half chicken laying eggs, one chicken will suffice in this problem.

Somehow I doubt that’s what the originator of the riddle wanted.

These are the sorts of problems in the barnyard that spurred Old MacDonald to write the seminal book The Mythical Chicken Day.

Well done Glowacks. A man after my own heart.

I am happy to accept your highly rational solution. It follows the same principles as mine, so it must be right … :wink:

People like us are lateral thinkers. We do not accept the obvious answer, we question the question. All human development comes from people like us, not from those who slavishly follow what they are meant to think and do.

The optimist thinks the glass is half full. The pessimist thinks it’s half empty. We wonder why they didn’t use a smaller glass.:cool:

I remember a parallel problem years ago.

A traveller is on a ship approaching a country. He knows there is a law in the country, that members of one sex must lie and members of the other sex tell truth, but he can’t remember which. Seeing a local man on shore, he shouts, “Do you tell the truth?” The man answers, but he can’t hear the answer because of the noise of wind and surf. A woman from the same country is beside him on the ship, and the traveller asks her, “What did he say?”. The woman replies, “He said he tells the truth.”

Who tells the truth? The mathematician says, “When asked the first question, every local person will claim to tell the truth. If the woman says this, she is telling the truth. Women tell truth and males lie.”

The lateral thinker’s view is different. Why should the woman on the ship hear better than the traveller? She pretended to hear what was said, and lied about it. Local men tell the truth, not women.

In any case, we know that the man on shore probably said, “What did you say? I can’t hear you.” If she heard him, the woman on the ship lied about this. So, again, local men tell the truth, not women.

Reality is logical, but not mathematical.

I apologise for my sexist assumption that Glowacks is male.:smack:

Well since you considered him to be telling the truth, that was a logical assumption.
Powers &8^]

And then we drink the water while the other two are arguing over it. :smiley:

Of course a half a chicken can lay half an egg. The right half of a chicken lays the right half of the egg, and the left half of the chicken lays the left half of the egg. Sure, a chicken that’s been chopped apart can’t lay anything, but the problem said nothing about butchers’ knives. Just leave the halves of the chicken firmly attached to each other, and there’s no problem.

I’ve got a runway to sell you guys

Sure, a half chicken can’t lay eggs, but if you have a factory farm, you can certainly have an AVERAGE of 1.5 chickens laying 1.5 eggs, etc.Which is totally relevant if one is trying to calculate cost/profit margins or some other such accounting issue.

OK, here’s my analysis purely as a logical problem.

If a chicken and a half can lay an egg and a half in a day and a half, then that same chicken and a half can lay another egg and a half every following day and a half. So, after three days (two days and two halves) it has laid three eggs (two eggs and two halves), and after six days it has laid six eggs.

All that assumes is that you can count two half eggs as one egg, and makes no assumptions about how half a chicken can do anything except lie dead, or about how any number of chickens can lay a half egg. We are given that as the premise of a logical puzzle. If you had a puzzle saying, “If two unicorns have two horns, how many unicorns do you need for six horns?”, the correct answer is “six unicorns”, and not “unicorns do not exist.”