this makes me giddy with joy for some reason

And that makes my rattle tingle!

Sure, I could use combinatorics and Principle of Inclusion-Exclusion, but I'm feeling lazy and it's 1 AM.

So we have the givens (reordered because the listings are best-first, so this makes it a little easier to work with) :
Henning > Eike
Henning > Paulie
Franz > Henning
Lars > Paulie

So, from the givens, Henning must appear in one of the first three slots (because at the very least, he beats Eike and Paulie) but cannot appear in the first slot (because Franz must come before him).
Similarly, Franz must appear in one of the first two slots because he must appear before Henning.

So, there become three ways to place these two: FH___, F_H__, _FH__.

In the first one, we know Lars must come before Paulie, but that's it. This gives us: FHLPE, FHLEP, and FHELP.
In the second, since Lars must come before Paulie, we have only two choices: FLHPE, and FLHEP.
In the third, we similarly only have two choices: LFHPE, and LFHEP.

Therefore, there are seven possible linearizations, and only one of them allow for Eike to end up ahead of Lars. So Eike's chances are 1/7 without any further information. (Analyzing relative performance of the Lars v Paulie match to the Henning v Paulie might help determine whether Lars can beat Henning, a vital component in determining odds. If Lars is unlikely to be able to beat Henning, let alone Franz, then Eike's chances jump to being 1/3.)

Extra Credit:
What is the minimal number of matches necessary to determine the final linearization? As in, how many matches do the brothers need to make time for in order to be certain to establish pecking order? (Sorry, couldn't resist the pun. ^_~ )

The main wildcard ends up being Lars, since he's the only one that still has a chance to be in the first two slots.
L ? F, Eliminates 5 is L > F, 2 if L < F.
L ? H, Eliminates 4 if L > H, 3 if L < H.
L ? E, Eliminates 1 if L > E, 6 if L < E.

Now, if we knew Eike would beat Lars, then the only match needed would be Lars vs Eike. However, we don't know, so that's not the minimum. The best bet would be to pit Lars against Henning, since the worst case will cut the possibilities to 4 (log_2(4) = 2). Since ceiling(log_2(7)) is three, there is no set of matches that will guarantee getting below 3.

FLHPE, FLHEP, LFHPE, LFHEP | FHLPE, FHLEP, FHELP

From here, worst case dictates Franz vs Lars and Paulie vs Eike. So, worst case is three matches.
The best case would need either Eike vs Paulie or Lars vs Eike. Unfortunately, each of those can leave behind two possibilities, so a third match might be necessary. So the minimum is still 3. Since we know we can't get a better answer, any other path can give us three or more, but we already have a path to give us at most three, so there's no point in searching more.

In fact, since both Lars vs Franz and Lars vs Eike both might leave more than 4 possibilities, you can't guarantee needing only three matches if you pick either of those first.

Since they were able to hold four matches today, they should be able to determine final outcomes tomorrow.

Should they change their mind and let you (or Celeste) play, it would only need a maximum of three matches to place the newcomer, since there would be six possible places. ...Assuming you don't turn any into statues during gameplay. ^_~

I like math too, though I only went for a minor in it, I didn't major in it.

You were quite a bit more thorough than I was. (I can't say how pleased I am that someone really dug into it! I wasn't counting on that.)

I agree on three matches being sufficient to settle everything as long as choices are made wisely. I have to say I'm a bit curious where the logarithm base 2 came from...if you minored in math, did you major in computer science?

And of course "pecking order" occurred to me as well. :>

Yes, I did major in Computer Science. The log_2 is because any choice can, at best, cut the possibilities in half. You'll have to cut it in half until you end up with only one possibility in both cases, which is log_2 times. It makes it akin to a Binary Search, because the "reality" is already sorted, but you're trying to find the position of a player by comparing them to someone in the middle, then deciding which portion of the list to check. ^_^

That's kind of what I thought, but I wasn't sure. I hadn't looked at it that way before...I was able to squeak by without any programming back in my era. That's not the case anymore.

I also used to play a game back in the days of DOS called "Sherlock", which is a giant Constraint Satisfaction Problem. There are six rows (People, Houses, Numbers, Fruit, Road signs, and Letters in the default tileset) and six colums, and a set of clues that you use to determine the position of each of the items. So a vertical clue that shows the red house above the apple means that those two are in the same column. (A text version of the puzzle would say something along the lines of "The person who eats apples lives in the red house." and so on.) A horizontal clue would tell you if things are adjacent, or to one side, or a couple other relations.

The "Franz is to the left of Henning" is what really kinda triggered this association in my mind, because it's similar to one of the types of clues in Sherlock.

Wow, you must have been the pick for group projects.

My issue with group projects was that I tended to get paired up with people who wouldn't pull their share of the work. That didn't always happen, but it was pretty often. ^_^;;

For Networks, the project was a distributed file server system, with multiple back end servers hosting the files, a front end server to handle client requests and do load-balancing, and a client to be able to request files. In the group of four, two of our team members weren't very helpful (one wouldn't show up for half the meetings, and spent most of the meetings he did show up for either making jokes or messing with installing Linux on whatever computers he could cobble together out of spare parts, and the other would just ask questions constantly about the things you just explained to the group). We kept running into problems because of an uncaught problem in our base Connection class (which we tested, but apparently not thoroughly enough) and on the day before it was due, we ended up scrapping the whole thing and starting over from scratch. The teammate who was helpful apparently broke down at that point, and walked out of the room. That was the last we ever saw of him, he dropped out and moved a couple states over. I ended up redoing the entire project in about eight hours, though without some of the nicer features that we had in the first version...

That's probably the worst group project I've ever been on. ^_^;;

Yeah, that's one of the reasons I hated having to do group projects in college.

wha @_@

Take deep breaths...relax.

TOO MUCH MATH! *flail*

I feel like I'm back in high school.

Is that a good thing or a bad thing? :>

Seriously, partial orders and elementary probability are something I think they should teach to middle school kids. Combinatorics is a lot more useful in every day life than Algebra is.

(I'll admit it: it still isn't terribly useful. But it leads to things like lotteries and gambling, which a lot of people seem to have passing interests in following.)

Is that a good thing or a bad thing? :>

I guess it depends. My schooling was full of terribly complex and stunted academic growth. In grade school, I was the class pick on. The one who always had cooties and was chosen last for kickball. Yep, that scrawny kid nobody liked or wanted to be friends with... was me.

*looks down at himself* What the hell happened to that kid anyway?

So... when I couldn't see the chalkboard in third grade, I said nothing because I didn't want to add anymore attention to myself as having something wrong. It wasn't till fifth grade that my parents learned I needed glasses, and by then I was horribly behind (C's were common place on my report card). I didn't pass the placement test to get into Algebra, but was pushed though anyway. Passed the Geometry readiness test, and excelled. Didn't pass the Algebra II test, but was again pushed through. Passed the Pre-Calculus test and did well, finishing out my senior year excelling at Calculus. Though throughout high school, I struggled keeping up with math. Was great at Trigonometry and Geometry, not so great at advanced Algebra.

When I went through my industrial electrician apprenticeship and math became a integral part of the early stages, I was far ahead of the curve while others struggled mightily with basic Algebra and Trigonometry.

So I like math, but because of personal struggles and limitations, math and me didn't always get along very well.

The answer is B) Buy Hauke a box of Cheez-its and a case of Kilt Lifter, and have him explain it to you. :)

I tried but I'm probably wrong: http://www.furaffinity.net/view/5990887/

Glad to see you're working on creative word problems; keep at it and maybe you'll make one you'll like enough to put on a test or handout.

Thanks for the illustrations! :>

No problem, I should start using your stories for drawing material. :)

you're really that fellow from the show 'Numbers' aren't you?

love it Hauke...

V.

Ew, no! I dislike that show...every time a mathematician appears in a movie or television show, there's got to be something bizarre about him...

I guess actually, I'm falling into that trap because here I am representing myself as a mutant chicken with supernatural powers...

*chuckles and gives him a hug... you're not a mutant to me.

That you can do these things (math) is a true gift.

V.