## One Third Bobcat

A forum for good logic/math puzzles.

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the_frufru
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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.

Macbi
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### 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 great-great-great-great 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 great-great-great-great 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 run-on sentence... then the only consistent scenario is that that cat is 1/3 bobcat.

Of course, the fact that real-world 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 perfect-blending 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)⚠);}`
[he/him/his]

Cauchy
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### Re: One Third Bobcat

It seems to me we should just

Spoiler:
determine the set of genes that distinguishes a bobcat from a house cat, and genetically engineer a creature that has all the genes bobcats and house cats have in common, a third of the genes differentiating the bobcat, and two-thirds of the genes differentiating a house cat.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
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jestingrabbit
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### Re: One Third Bobcat

Cauchy wrote:It seems to me we should just

Spoiler:
determine the set of genes that distinguishes a bobcat from a house cat, and genetically engineer a creature that has all the genes bobcats and house cats have in common, a third of the genes differentiating the bobcat, and two-thirds of the genes differentiating a house cat.

I liked the time traveling answer better. It has more zing, pizzazz and... stuff.
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Patashu
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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.

Apolsis
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### 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."
-Oscar Wilde, "The Canterville Ghost"

dan
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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.

Puck
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### Re: One Third Bobcat

"SWM seeks fun-loving nerd-girl for copulation, procreation. Non-smoker, non-drinker, 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% bob-cat, the others are domesticated cat kittens.
in ur beanz makin u eveel

Hix
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### Re: One Third Bobcat

Maybe the kittens are 1/3 bobcat, with the other 2/3 also being bobcat.

Buttons
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### 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.

eddiekizer
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### Re: One Third Bobcat

There are a few things I can think of:
Spoiler:
Practicality. Nobody will compliment you for announcing that your cats are exactly 332/1000 bobcat. It's much simpler to just say 1/3.

Spoiler:
Maybe the guy, oddly enough, is selling dismembered bobcat parts. But that's sick to think about.

Spoiler:
Or, as Cauchy said, it has something to do with genes/chromosomes.

Spoiler:
Lastly, maybe one of the cats was born as the result of a three-way (of, you know, well yeah). But that's sick too.
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Citizen K
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### 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 one-third bobcat and two-thirds 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)
Beware the cows! Not all milk is enriched.

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?

nishikigoi
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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.

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, already-odd-fractional-breed 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 cross-generational breeding, or whatever).

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
[he/him/his]

nishikigoi
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### Re: One Third Bobcat

Curse you, Excel!

AvalonXQ
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### Re: One Third Bobcat

Easy:
Spoiler:
just assume that the 1/3 refers to phenotype. The kitten may be 1/2 or 1/4 bobcat by genotype but have a number of expressed genetic traits divisible by 3, of which bobcat is expressed 1/3 and recessed 2/3s of the time.

flippmoke
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### Re: One Third Bobcat

Maybe the person can't do math?

Lord Aurora
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### Re: One Third Bobcat

flippmoke wrote:Maybe the person can't do math?
I'm pretty much certain that this was assumed from the start.
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fyjham
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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.

qetzal
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### Re: One Third Bobcat

I think this would count as exacty 1/3 bobcat:

Spoiler:
First, breed a tetraploid housecat. Then breed it to a normal diploid bobcat. The offspring will have two sets of housecat chromosomes and one set of bobcat chromosomes.

nishikigoi
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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...

notgm
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### Re: One Third Bobcat

flippmoke wrote:Maybe the person can't do math?

i'm voting for this option. 2/3 majority rules.

fyjham
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### 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?

Kain
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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)
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...
Look, you know it's serious when a bunch of people in full armor and gear come charging in to fight a pond of chickens - Steax

qetzal
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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.

Spoiler:
Breeding a tetraploid housecat would be a big challenge, but there's at least some evidence it could be possible. On the one hand, people have tried to breed tetraploid lab mice, so far without success (e.g., http://www.ncbi.nlm.nih.gov/pubmed/16246322). OTOH, there is at least one naturally occuring tetraploid mammal: http://www.ncbi.nlm.nih.gov/pubmed/18758856.

Assuming you could breed a tetraploid housecat, you'd still need to successfully breed it to a normal bobcat. That may also be difficult. The difference in ploidy could prevent successful embryo development.

Nevertheless, it's at least possible, and if successful would give you kittens with exactly 2/3 housecat DNA + 1/3 bobcat DNA.

Kain
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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
Look, you know it's serious when a bunch of people in full armor and gear come charging in to fight a pond of chickens - Steax

scrovak
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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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AvalonXQ
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### Re: One Third Bobcat

Again, time travel. Time travel solves everything.

hocl
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### Re: One Third Bobcat

Perhaps the maker of the sign comes from a dystopian world where, under threat of overpopulation despite attacks from hive-mind, insect-like 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, paragraph-length 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.

Vieto
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### Re: One Third Bobcat

Maybe it only tears up one third of you're face when you take it out of the packaging...

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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".
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

H2SO4
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### 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 half-bobcat 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.

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
[he/him/his]

Foolish Mortal
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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.

qetzal
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### 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....