# 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 **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [March 14, 2013, 2:40pm UTC](https://boards.straightdope.com/t/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/652918 "2013-03-14T14:40:23Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![fatboy](https://avatars.discourse-cdn.com/v4/letter/f/49beb7/32.png) [@fatboy](https://boards.straightdope.com/u/fatboy)\ **Post date:** [March 14, 2013, 2:40pm UTC](https://boards.straightdope.com/t/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/652918/1 "2013-03-14T14:40:23Z")
[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](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. ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [March 14, 2013, 7:36pm UTC](https://boards.straightdope.com/t/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/652918/2 "2013-03-14T19:36:40Z")
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. ---
**Author:** ![Jack\_Batty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jack_batty/32/3201_2.png) [@Jack\_Batty](https://boards.straightdope.com/u/Jack_Batty)\ **Post date:** [March 14, 2013, 7:39pm UTC](https://boards.straightdope.com/t/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/652918/3 "2013-03-14T19:39:33Z")
Personally, I think half a hen would lay still. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [March 14, 2013, 7:50pm UTC](https://boards.straightdope.com/t/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/652918/4 "2013-03-14T19:50:49Z")
I think the best response to any question about “half chickens” laying “half eggs” is to smile and back away slowly. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [March 14, 2013, 8:28pm UTC](https://boards.straightdope.com/t/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/652918/5 "2013-03-14T20:28:55Z")
Does second base count as half laid? ---
**Author:** ![dstarfire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dstarfire/32/5762_2.png) [@dstarfire](https://boards.straightdope.com/u/dstarfire)\ **Post date:** [March 14, 2013, 8:53pm UTC](https://boards.straightdope.com/t/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/652918/6 "2013-03-14T20:53:21Z")
> [@Irishman](#): > > 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. 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. ---
**Author:** ![squidfood](https://avatars.discourse-cdn.com/v4/letter/s/a87d85/32.png) [@squidfood](https://boards.straightdope.com/u/squidfood)\ **Post date:** [March 14, 2013, 10:51pm UTC](https://boards.straightdope.com/t/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/652918/7 "2013-03-14T22:51:44Z")
> [@Czarcasm](#): > > I think the best response to any question about “half chickens” laying “half eggs” is to smile and back away slowly. As a biostatistician, I can confidently say that you _never_ end up with a whole number of chickens. I got 1.500031521 +/- 3.305. ---
**Author:** ![dotchan](https://avatars.discourse-cdn.com/v4/letter/d/9d8465/32.png) [@dotchan](https://boards.straightdope.com/u/dotchan)\ **Post date:** [March 15, 2013, 1:59am UTC](https://boards.straightdope.com/t/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/652918/8 "2013-03-15T01:59:12Z")
Maybe it’s a Schrodinger’s egg, it’s either there or not there depending on who observes it? ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [March 15, 2013, 8:59pm UTC](https://boards.straightdope.com/t/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/652918/9 "2013-03-15T20:59:32Z")
> [@Czarcasm](#): > > I think the best response to any question about “half chickens” laying “half eggs” is to smile and back away slowly. 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. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [March 15, 2013, 9:19pm UTC](https://boards.straightdope.com/t/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/652918/10 "2013-03-15T21:19:08Z")
> [@Irishman](#): > > 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.](http://www.youtube.com/watch?v=KTwnwbG9YLE) ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [March 15, 2013, 9:54pm UTC](https://boards.straightdope.com/t/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/652918/11 "2013-03-15T21:54:00Z")
> [@Czarcasm](#): > > [It’s a joke, son.](http://www.youtube.com/watch?v=KTwnwbG9YLE) Stop that! 😉 ---
**Author:** ![Nametag](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nametag/32/406_2.png) [@Nametag](https://boards.straightdope.com/u/Nametag)\ **Post date:** [March 16, 2013, 7:38am UTC](https://boards.straightdope.com/t/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/652918/12 "2013-03-16T07:38:03Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 16, 2013, 6:11pm UTC](https://boards.straightdope.com/t/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/652918/13 "2013-03-16T18:11:31Z")
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. ---
**Author:** ![moriah](https://avatars.discourse-cdn.com/v4/letter/m/b2d939/32.png) [@moriah](https://boards.straightdope.com/u/moriah)\ **Post date:** [March 16, 2013, 8:44pm UTC](https://boards.straightdope.com/t/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/652918/14 "2013-03-16T20:44:26Z")
If you put three chickens in a Shrodinger’s box… ---
**Author:** ![pseudotriton\_ruber\_ruber](https://avatars.discourse-cdn.com/v4/letter/p/a9a28c/32.png) [@pseudotriton\_ruber\_ruber](https://boards.straightdope.com/u/pseudotriton_ruber_ruber)\ **Post date:** [March 16, 2013, 9:04pm UTC](https://boards.straightdope.com/t/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/652918/15 "2013-03-16T21:04:12Z")
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?” ---
**Author:** ![sunnyone](https://avatars.discourse-cdn.com/v4/letter/s/50afbb/32.png) [@sunnyone](https://boards.straightdope.com/u/sunnyone)\ **Post date:** [March 19, 2013, 7:10am UTC](https://boards.straightdope.com/t/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/652918/16 "2013-03-19T07:10:14Z")
Is the chicken half empty or half full? ---
**Author:** ![GTPhD1996](https://avatars.discourse-cdn.com/v4/letter/g/97f17d/32.png) [@GTPhD1996](https://boards.straightdope.com/u/GTPhD1996)\ **Post date:** [March 20, 2013, 6:18pm UTC](https://boards.straightdope.com/t/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/652918/17 "2013-03-20T18:18:25Z")
> [@sunnyone](#): > > 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. ---
**Author:** ![RedSwinglineOne](https://avatars.discourse-cdn.com/v4/letter/r/a9adbd/32.png) [@RedSwinglineOne](https://boards.straightdope.com/u/RedSwinglineOne)\ **Post date:** [March 20, 2013, 6:51pm UTC](https://boards.straightdope.com/t/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/652918/18 "2013-03-20T18:51:40Z")
“First, let’s assume spherical chickens.” ---
**Author:** ![CJJ](https://avatars.discourse-cdn.com/v4/letter/c/ecc23a/32.png) [@CJJ](https://boards.straightdope.com/u/CJJ)\ **Post date:** [March 20, 2013, 6:53pm UTC](https://boards.straightdope.com/t/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/652918/19 "2013-03-20T18:53:09Z")
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”. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [March 20, 2013, 7:06pm UTC](https://boards.straightdope.com/t/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/652918/20 "2013-03-20T19:06:09Z")
> [@Jack\_Batty](#): > > Personally, I think half a hen would lay still. 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. [Next page](https://boards.straightdope.com/t/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/652918.md?page=2)