One Third Bobcat
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One Third Bobcat
Driving home one night, I noticed a sign on the side of the road advertising "For Sale: One third bobcat kittens." I didn't think much of it, beside the obvious physiological difficulties of breeding house cats and bobcats.
It ate at me, then I realized why, even if they could breed, it is impossible. Now, I ask this question to all of my interviewees at my company.
It ate at me, then I realized why, even if they could breed, it is impossible. Now, I ask this question to all of my interviewees at my company.
Re: One Third Bobcat
No, but you can approach 1/3 as a limit. Much like you can with hybrid sporks.
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 Lord Aurora
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Re: One Third Bobcat
Macbi wrote:No, but you can approach 1/3 as a limit. Much like you can with hybrid sporks.
Exactly what I was thinking. Say you went back to a set of ancestors of the cat (all of its greatgreatgreatgreat grandparents, for example) such that the number of ancestors was 100. 33 of them could be bobcats, making the cat 1/3 bobcat for all intents and purposes, but not in the technical sense.
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 phlip
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Re: One Third Bobcat
Lord Aurora wrote:Exactly what I was thinking. Say you went back to a set of ancestors of the cat (all of its greatgreatgreatgreat grandparents, for example) such that the number of ancestors was 100.
Well, it's not going to be 100 either... it's going to be a power of two. (Well, you could have less if there's some inbreeding going on, but all that means is that some of the ancestors count twice... you'll still end up with a power of two on the denominator.)
However, this assumes a lack of time travel... if any of the cats is capable of being its own ancestor, then the argument breaks down. If a cat goes back in time, and procreates with a purebread bobcat... then its child procreates with a purepread housecat of some kind, and that child goes back in time and turns out to be the cat I mentioned at the start of this runon sentence... then the only consistent scenario is that that cat is 1/3 bobcat.
Of course, the fact that realworld genetics is discrete, and that there's random chance involved in which grandparent's genes you get from each parent... not to mention mutations... kinda makes all this discussion about perfectblending continuous genetics moot anyway.
For entirely too much information, check out the discussion thread for the "sporks" comic, as a couple of people have mentioned... this has been discussed to death in there.
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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵╰(ಠ_ಠ ⚠) {exit((int)⚠);}
Re: One Third Bobcat
It seems to me we should just
Spoiler:
(∫p^{2})(∫q^{2}) ≥ (∫pq)^{2}
Thanks, skeptical scientist, for knowing symbols and giving them to me.
Thanks, skeptical scientist, for knowing symbols and giving them to me.
 jestingrabbit
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Re: One Third Bobcat
Cauchy wrote:It seems to me we should justSpoiler:
I liked the time traveling answer better. It has more zing, pizzazz and... stuff.
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Re: One Third Bobcat
Just keep breeding for millenia and see if you can select towards a sexual method of reproduction involving three distinct genders.
I mean, if you have a couple million years to blow.
I mean, if you have a couple million years to blow.
Re: One Third Bobcat
"Indeed, in may respects, she was quite English, and was an excellent example of the fact that we have really everything in common with America nowadays, except, of course, language."
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Re: One Third Bobcat
I like telling people I'm a third Irish for this reason  it's interesting to see if they notice. Of course it's probably closer to five sixteenths. Thanks to this thread I will probably end up taking this into account when weighing up future relationships... I have a strange desire to get any kids of mine as close to a third as possible now.
Re: One Third Bobcat
"SWM seeks funloving nerdgirl for copulation, procreation. Nonsmoker, nondrinker, between 1/4 and 1/2 Irish heritage. 17/48 ideal!!"
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 JamesCFraser
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Re: One Third Bobcat
the_frufru wrote:Now, I ask this question to all of my interviewees at my company.
You interview people for the position of janitor?
Seriously, though. Incredibly trivial question
 evilbeanfiend
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Re: One Third Bobcat
perhaps the sign refers to 1/3 averaged over all the kittens for sale i.e. 1 in every 3 kittens for sale is 100% bobcat, the others are domesticated cat kittens.
in ur beanz makin u eveel
Re: One Third Bobcat
Maybe the kittens are 1/3 bobcat, with the other 2/3 also being bobcat.
Re: One Third Bobcat
JamesCFraser wrote:Seriously, though. Incredibly trivial question
Maybe, but there are obviously different levels of responses, as this thread demonstrates. You can certainly learn something about the interviewee's thought process.

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Re: One Third Bobcat
There are a few things I can think of:
Spoiler:
Spoiler:
Spoiler:
Spoiler:
I plugged a Mac into a cat,
And plugged a PC into a dog.
Then the penguin that runs on Linux
Came and ate them.
And plugged a PC into a dog.
Then the penguin that runs on Linux
Came and ate them.
Re: One Third Bobcat
Or, maybe the sign was referring to a group of kittens for sale (say, 9), one third of which were bobcats (say, 3). Not necessarily from the same parents. It's a bit of a stretch, but I don't think it's unreasonable. Handwritten sale signs are not always known for their clarity.
Some possible interpretations of the sign:
Each kitten is genetically onethird bobcat and twothirds housecat.
One third of the available kittens are bobcats and two thirds of them are housecats.
The owners have a litter of bobcat kittens, and one third of them are for sale.
Each item for sale is literally one third of a bobcat kitten. (eeeew)
Some possible interpretations of the sign:
Each kitten is genetically onethird bobcat and twothirds housecat.
One third of the available kittens are bobcats and two thirds of them are housecats.
The owners have a litter of bobcat kittens, and one third of them are for sale.
Each item for sale is literally one third of a bobcat kitten. (eeeew)
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 Godskalken
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Re: One Third Bobcat
Hix wrote:Maybe the kittens are 1/3 bobcat, with the other 2/3 also being bobcat.
Definitely this.
Or possibly the "added 's' accent", you know, from "anyways" etc. That is, what it actually says is "one third bobcat kitten", as in "one half chicken". Was the sign outside a chinese restaurant perchance?

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Re: One Third Bobcat
Thanks for nothing, folks. I had a pretty decent existence until someone had to go and suggest that a kitten could be 1/3 bobcat. Now it's 11:30 pm, and I'm running calculations in an Excel sheet trying to figure out if such a thing might ever be possible.
Let's ignore for the moment phlip's notion of bobcat time travel. I shudder to imagine the implications of such a possibility. Time travel aside, the number of ancestors for a kitten who is 1/3 bobcat cannot be 100. The kitten has two parents who each have two parents who have two parents, etc. The genetic tree doubles every time we go back a generation.
To get a generation in which the number of ancestors is divisible by 3, we have to go back 49 generations. (The litter of 1/3 bobcat kittens is the 50th generation.) At this point, our improbable kitten has 562949953421312 ancestors in a single generation. (If you're curious, the total number of ancestors for our kittens is now 1125899906842620.)
If our kitten's genetic heritage can now be expressed in a fraction with a denominator divisible by 3, wouldn't it be possible for the product of their breeding, 49 generations later, to be 187649984473771/562949953421312 (or 1/3) bobcat?
This is where I get lost. I can't figure out how to create a mathematical model showing how the breeding would yield something that was 1/3 bobcat. Please help. I'm quite certain that I will lose sleep over this.
Let's ignore for the moment phlip's notion of bobcat time travel. I shudder to imagine the implications of such a possibility. Time travel aside, the number of ancestors for a kitten who is 1/3 bobcat cannot be 100. The kitten has two parents who each have two parents who have two parents, etc. The genetic tree doubles every time we go back a generation.
To get a generation in which the number of ancestors is divisible by 3, we have to go back 49 generations. (The litter of 1/3 bobcat kittens is the 50th generation.) At this point, our improbable kitten has 562949953421312 ancestors in a single generation. (If you're curious, the total number of ancestors for our kittens is now 1125899906842620.)
If our kitten's genetic heritage can now be expressed in a fraction with a denominator divisible by 3, wouldn't it be possible for the product of their breeding, 49 generations later, to be 187649984473771/562949953421312 (or 1/3) bobcat?
This is where I get lost. I can't figure out how to create a mathematical model showing how the breeding would yield something that was 1/3 bobcat. Please help. I'm quite certain that I will lose sleep over this.
 phlip
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Re: One Third Bobcat
187649984473771/562949953421312 isn't 1/3... it's very close, but it's not quite (187649984473771 * 3 = 562949953421313). It's probably the fault of your spreadsheet software, which is starting to round off at this point.
Suffice it to say that, sans time travel, alreadyoddfractionalbreed initial ancestors, or genetic abnormalities (somehow getting more genes from one parent than the other), the fraction of any breed will be dyadic. This is the case regardless of how far back you engineer the tree, how many ancestors there are, how twisted the family tree is (with individual ancestors appearing more than once, or crossgenerational breeding, or whatever).
Suffice it to say that, sans time travel, alreadyoddfractionalbreed initial ancestors, or genetic abnormalities (somehow getting more genes from one parent than the other), the fraction of any breed will be dyadic. This is the case regardless of how far back you engineer the tree, how many ancestors there are, how twisted the family tree is (with individual ancestors appearing more than once, or crossgenerational breeding, or whatever).
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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵╰(ಠ_ಠ ⚠) {exit((int)⚠);}
Re: One Third Bobcat
Maybe the person can't do math?
 Lord Aurora
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Re: One Third Bobcat
I'm pretty much certain that this was assumed from the start.flippmoke wrote:Maybe the person can't do math?
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Re: One Third Bobcat
flippmoke wrote:Maybe the person can't do math?
But surely in logic puzzles it's safe to assume all people are perfectly rational unless stated otherwise... right?
Perhaps the owner of the house is a mad scientist and has been following in the footsteps of Dr Frankenstein and built a kitten that turned out to be 1/3rd bobcat from the parts of other dead kittens.
It's sort of bugging me though how you can get this question into an interview without wording it in a way that makes 1/3rd bobcat obviously the problem... that and whether any of your interviewee's have proposed some of the more peculiar answers provided here
btw nishikigoi: 2^n can never be divisible by 3, no matter how high of a power of 2 you reach. Simplest way to prove it is that 3's a prime number, so once you reduce something to it's prime factors 3 should be one of them if it's divisible. 2^n only has 2 (n times) as it's prime factors.
Re: One Third Bobcat
I think this would count as exacty 1/3 bobcat:
Spoiler:

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Re: One Third Bobcat
fyjham wrote:btw nishikigoi: 2^n can never be divisible by 3, no matter how high of a power of 2 you reach. Simplest way to prove it is that 3's a prime number, so once you reduce something to it's prime factors 3 should be one of them if it's divisible. 2^n only has 2 (n times) as it's prime factors.
Thank you, fyjham. My liberal arts education didn't put much emphasis on math...
Re: One Third Bobcat
flippmoke wrote:Maybe the person can't do math?
i'm voting for this option. 2/3 majority rules.
Re: One Third Bobcat
notgm wrote:i'm voting for this option. 2/3 majority rules.
So are you saying that since it's 2/3rds housecat it's not a bobcat at all?

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Re: One Third Bobcat
You are all missing an obvious means of arriving at 1/3 heritage (or at least what someone might claim as 1/3 heritage)
You start with 1 male bobcat (Adam) and two female bobcats (Beth and Cindy).
Adam and Beth have a litter of kittens together, including a male kitten (Dale), while Adam and Cindy have a litter of kittens that includes a female kitten (Edith). Wait a few months to a year, and Dale and Edith have a litter of 1/3rd Bobcat kittens.
Now wait, you say: Dale and Edith are both 1/2 bobcat, so clearly their kittens are also 1/2 bobcat, right?
Yes and No: Genetically speaking they are probably close to 1/2 bobcat, if such a distinction is even possible. However, out of the three distinct grandparents of the kittens, only one is a Bobcat. Thus, 1/3 bobcat...
You start with 1 male bobcat (Adam) and two female bobcats (Beth and Cindy).
Adam and Beth have a litter of kittens together, including a male kitten (Dale), while Adam and Cindy have a litter of kittens that includes a female kitten (Edith). Wait a few months to a year, and Dale and Edith have a litter of 1/3rd Bobcat kittens.
Now wait, you say: Dale and Edith are both 1/2 bobcat, so clearly their kittens are also 1/2 bobcat, right?
Yes and No: Genetically speaking they are probably close to 1/2 bobcat, if such a distinction is even possible. However, out of the three distinct grandparents of the kittens, only one is a Bobcat. Thus, 1/3 bobcat...
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Re: One Third Bobcat
Kain,
You should really count the grandparents as Adam, Beth, Cindy, and Adam again. Adam counts twice. So you still have 1/2 bobcat, 1/2 house cat. (You meant for Beth and Cindy to be house cats, right?)
I still think my approach (above) is the only way to get genetically exactly 1/3 bobcat.
You should really count the grandparents as Adam, Beth, Cindy, and Adam again. Adam counts twice. So you still have 1/2 bobcat, 1/2 house cat. (You meant for Beth and Cindy to be house cats, right?)
I still think my approach (above) is the only way to get genetically exactly 1/3 bobcat.
Spoiler:

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Re: One Third Bobcat
qetzal,
you are probably right from the standpoint of any intelligent approach to this, but remember from the OP that this is a 1/3 bobcat kitten breeder here... who knows what they were thinking, lolz
you are probably right from the standpoint of any intelligent approach to this, but remember from the OP that this is a 1/3 bobcat kitten breeder here... who knows what they were thinking, lolz
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Re: One Third Bobcat
This is true. Because ancestry is exponential by a factor of 2, it is impossible to have 1/3 anything.
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Re: One Third Bobcat
Again, time travel. Time travel solves everything.
Re: One Third Bobcat
Perhaps the maker of the sign comes from a dystopian world where, under threat of overpopulation despite attacks from hivemind, insectlike aliens with instantaneous psychic bonds, families are under a strict prohibition against having more than two children, to the point where the term "third" becomes a disparaging term for a child born in violation of that policy, with a rare exception being made for a particular couple who are expected to give birth to a brilliant military strategist, and with said child being trained from a young age to defeat the alien invaders, but, having achieved victory, constituting such a destabilizing force for the victorious but fractious surviving societies that he is forced to travel to another world, said other world being our own, where through a coincidence of parallel evolution, his features bear a remarkable resemblance to those of bobcats in this world, resulting in his children being advertised as "one third bobcat kittens", and prompting speculation that is ultimately explained through an absurdly long, paragraphlength sentence. I mean, really, isn't that an obvious explanation?
Or maybe a female housecat had sex with two bobcats and housecat, making the children one third bobcat. Whichever seems more reasonable to you.
Or maybe a female housecat had sex with two bobcats and housecat, making the children one third bobcat. Whichever seems more reasonable to you.
Re: One Third Bobcat
Maybe it only tears up one third of you're face when you take it out of the packaging...
 MartianInvader
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Re: One Third Bobcat
The seller in question must have had several litters of bobcat kittens and decided to keep the first and second of each litter, and sell the third. So he was selling third bobcat kittens. The sign probably originally said something like "For sale: Five third bobcat kittens". Of course, that was when five were availbable, and third bobcat kittens being the hot commodity they are, they were bought fairly quickly. So he had to keep going back to readjust the sign: "Four third bobcat kittens", "three third bobcat kittens", etc. Now he's down to the last one, but forgot to erase the pluralization from the end. Thus the sign:
"For sale  One third bobcat kittens".
"For sale  One third bobcat kittens".
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!
Re: One Third Bobcat
phlip wrote:187649984473771/562949953421312 isn't 1/3... it's very close, but it's not quite (187649984473771 * 3 = 562949953421313). It's probably the fault of your spreadsheet software, which is starting to round off at this point.
But that could then be a point someone brought up earlier, how no one is impressed when you say that it's 332/1000 bobcat, and for all intents and purposes it's 1/3 bobcat. Unless there is some kind of medicine that has a dosage based on genetics that would be thrown off by .0000000000000177635, and therefore would kill your kitten that is 187649984473771/562949953421312 bobcat... That'd be interesting.
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 phlip
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Re: One Third Bobcat
H2SO4 wrote:and for all intents and purposes it's 1/3 bobcat.
Well, for all intents and purposes except pedantry... which is really the only reason this thread exists in the first place.
If you want to bring in genetics, it all changes anyway... a cat with three housecats and one bobcat for grandparents could be anywhere between 0% and 50% bobcat, genetically, depending on which genes it gets from its halfbobcat parent (each chromosome has a 50% chance of being housecat or bobcat, but independantly, so it could be all one, or the other... a bit more complicated with crossover, but the range still holds). 1/3 bobcat is quite possible here, if there are a multiple of 3 chromosomes (or a multiple of 3 genes, and we're taking crossover into account). But it'll still be conventionally called "1/4 bobcat", since 1 of its 4 grandparents is a bobcat.
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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
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Re: One Third Bobcat
Maybe it's a quantum bobcat. Like, the guy put a female housecat in a box with two male bobcats and one male housecat, and when he took the female out she was pregnant. The resulting litter would be simulataneously half bobcat, half bobcat, and full housecat, which works out as one third bobcat by my estimation.
Re: One Third Bobcat
@ Foolish Mortal,
I like it!
Of course, the kits will only be 1/3 bobcat until they're born (or maybe until someone does an ultrasound?). Then the wavefunction will collapse to either 1/2 bobcat (P = 2/3) or full housecat (P = 1/3).
But until then....
I like it!
Of course, the kits will only be 1/3 bobcat until they're born (or maybe until someone does an ultrasound?). Then the wavefunction will collapse to either 1/2 bobcat (P = 2/3) or full housecat (P = 1/3).
But until then....
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