A very silly logic puzzle

[Carillon]

Apologies in advance. This is a very silly little logic puzzle. We'll say that it's in honor of the new character approvers.

A new character submission describes the family relations of a female elf. She has three full siblings (same mother and father) and no half siblings. She has one half-elven brother, one half-elven sister, and a human brother.

What were the races of her mother and father, respectively?

Feel free to post your answer. First person to solve it gets a cookie! Well no, not really. But you can give yourself a cookie.

[Stephen_Zuckerman]

They're both half-elves.

[Tialle Dianesis]

They were both Half-elves!



*points up* Shame! I was hoping to be the first.

[Stephen_Zuckerman]

..A..B A.AA.AB B.AB.BB

[Pseudonym]

Four kids? In today's dark ages?

The mother raced to have her head read and the father raced to the vasectomy clinic.

[Carillon]

Oooh, you two are just SO clever.

Okay, okay ... you may both give yourselves a cookie. This stemmed from the genetics report I'm writing tonight, and the very random thought that my character, Arynne, must be heterozygous for the "elf" gene (Pleiotropic for the traits of sleeplessness, good eyesight, and pointy ears!)



Very well, smartie pants-es. We'll try again.



Gloin Stoneaxe came from a proud dwarven family. One day, when Gloin was bathing in the river with some other young dwarves, he noticed that some of the dwarves had longer beards than others. In fact, it seemed like all the dwaves fell into one of three categories: long beard, short beard, or "normal" beard.

Curious, he asked his father what determined the length of a dwarf's beard .. apart from shaving it off, of course, which no dwarf in his right mind would ever do! His father replied by saying he didn't really know, but told him a story about his Grandma and Grandpa Stoneaxe. Grandma Stoneaxe was the hairiest female dwarf that had ever lived in their community. In fact, she was so hairy that her beard was even longer than Grandpa Stoneaxe's. Poor Grandpa Stoneaxe had almost no beard at all!

Even though they had such unusual parents, Gloin's Papa and all his aunts and uncles looked pretty much like the rest of the dwarves -- at least in terms of beard length -- and Gloin's Mom was pretty average for a lady dwarf too.

So .. can you figure out the chances that the next time Gloin goes bathing in the river, he'll feel pretty proud of his long beard? Or is it more likely he's normal or (gasp!) almost clean-shaven?

(And yes, if you've taken genetics, these are easy. Don't MAKE me break out the epistasis questions! )

[Pseudonym]

Is beard a euphemism? *Pseudonym squints suspiciously*

[Carillon]

No, no! I didn't mean it as a euphemism! Gah! I meant it in an Archimedes-in-the-bath sort of way!

Get your mind out of the gutter!

Err .. to prevent confusion, Gloin now made all his observations while bashing the other dwarves over the head with an empty tankard of ale. Though how he had the presence of mind to figure out dwarven genetics while drunk is beyond me


Edit: And as further justification that for once I meant this completely innocently, explain how his grandmother would have been hairier than her husband! Clearly in this case a beard is just a beard. Don't go all Freudian on me!

[Stephen_Zuckerman]

Alright... And this is all from my Highschool Biology class, a couple of years ago. (Also, we're making the assumption that the combination of the long beard and short beard genes make for a medium-beard child.)

If there are only two traits, neither of which is dominant, for a (short beard) and b (long beard), and the combination ab makes a medium-length beard, then he's got a 25% chance of having a long beard, 25% that it'll be really short, and 50% that he'll be average.

However... *Grins.* Here's where it gets interesting.

Three traits... One for short beards (a), one for long beards (b), and one for medium beards (the dominant trait C).

We know Gloin's father's match-up: ab.

Since we don't know Gloin's mother's genetic makeup, we can't make any assumptions about her, meaning there are four possible combinations for her: ab, Ca, Cb, and CC. Man, the permutations are going to be fun on this.

Once we've done the math (or written it out, like I did), we find out that we end up with sixteen possible combinations.

aa: 2/16
ab: 4/16
bb: 2/16
Ca: 4/16
Cb: 4/16

Now, technically I'm sure that's not perfect, as I think you're supposed to keep the order of the traits the same on all, but... Simplicity.

Let's recall: The dominant trait, C, causes a dwarf to have medium-length beards. Likewise, the combination ab causes the same. The combinations aa and bb cause long and short beards, respectively.

This means that, after a bit of counting, 12 of the 16 possible combinations would give Gloin a middling-length beard, 2 of the 16 would give him a long beard, and the other 2 of the 16 would give him a short beard.

A wee bit of computation later...

Short: 12.5%
Long: 12.5%
Medium: 75%