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

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

Hi,
Let me first say that I started reading SD only recently, and can’t believe how late to the party I am.

While the solution in the column is correct, we can get away without juggling fractions.
1.5 hens lay 1.5 eggs in 1.5 days
So the same number of eggs in the same number of days (are laid by 1.5 hens)

How many hens lay 6 eggs in 6 days? 1.5
How many hens lay x eggs in x days? 1.5

Thanks.

The essence of the problem: someone sees all the one and a halfs and decides they all cancel out, ergo they think 1 hen lays 1 egg in 1 day.

The heart of the problem as a math problem is that you can’t just cancel all the halfs simultaneously.

Of course there is the distraction of how a half a hen lays anything, etc.

Personally, I think half a hen would lay still.

I think the best response to any question about “half chickens” laying “half eggs” is to smile and back away slowly.

Does second base count as half laid?

I think the tricky part is actually that each of first 2 “one and a half”'s would, by themselves be greater than 1/day. (more eggs per chicken, or more chickens with one egg), but the “day and a half” actually reduces the rate. IF rate=total/time then total+n is a higher rate, but time+n is a lower rate.

As a biostatistician, I can confidently say that you never end up with a whole number of chickens. I got 1.500031521 +/- 3.305.

Maybe it’s a Schrodinger’s egg, it’s either there or not there depending on who observes it?

If your talking about rates of production, then it is certainly sensible to talk about producing 1.5 eggs per day. All that means is that, on average, it takes 2 days to lay 3 eggs. It does not mean that the egg takes ~ 16 hrs to pass through the cloaca.

Furthermore, if you are speaking about rates, then it is acceptable to vary the number of chickens involved for the comparison. One can look at per each chicken, or per 2 chickens, or per a dozen chickens.

What makes it sound funny is when you start taking those statistical quantities and then preface your question with a non-integer number of chickens. That sounds funny. “How does half a chicken do anything?” But realize it’s just a rearrangement of a rate statement. As a rate statement, it can be mathematically converted to a different rate base.

It’s a joke, son.

Stop that! :wink:

One and a half chickens is a time average. In reality, you have to start with two chickens, and strangle one on the morning of day four.

A half a chicken can lay half an egg, no problem. It just has to be attached to another half-chicken, which simultaneously lays the other half of the egg.

If you put three chickens in a Shrodinger’s box…

I always heard the second part of the question as, “then how many monkeys will it take to kick the seeds out of a dill pickle?”

Is the chicken half empty or half full?

Has the chicken laid the half egg yet? If yes, it is half empty. If no, it is half full.

“First, let’s assume spherical chickens.”

Kidding aside, the joke is structured so that all the numerical values match; “1.5 hens lay 1.5 eggs in 1.5 days” is mathematically equivalent to “1 hen lays 2 eggs in 3 days”. but the fractional form encourages the patsy to think the pattern is for all the values to match, so when you ask “How many days does it take for 6 hens to lay 6 eggs?” he’s tempted to quickly (and incorrectly) answers 6.

The fact that fractions are involved makes the temptation to follow a simpler pattern more alluring. I don’t think as many people would be fooled if you premised “1 hen lays 1 egg in 1 day”.

I agree. Half hens don’t lay eggs. So one hen is producing one egg and half an egg in a day and a half. Since we’re looking for six eggs, and not any half eggs, it would take two hens to lay six eggs in six days, plus you get two extra eggs and eight half eggs to boot.