A Riddle of Chess...

#11

QUOTE(Fapper @ Oct 26 2006, 12:10 PM) CDR!!!!!! "Simple" factorials that's a new term? you better pray to your God to make that true "32!=528"

yes, simple factorials, for excel compared to my general workload. hehe

you should see some of the hard stuff we do. Like this:

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You have 183 power schedulings from New York, each lasting 1 hour, all scheduled through the Midwest Independent System Operator (MISO) on the same day, and from there onto California, where you are going to help serve base load for California, and get alternative energy emissions credits for the wind farms you just bought. There are four open control areas to deliver the power, and every one of the 390 participants in the MISO region have available capacity storage to prevent congestion. How can you arrange 183 schedulings through four control areas, composed of 12 plants and two transmission specialists, while minimalizing capacity payments to the owners of those plants (the payment to store your energy while the lines are "full"), and keep energy loss below 3.2% (stored energy bleeds out of the capacitors).

AND also, don't forget to make sure that your own production for these orders doesn't exceed the general capacity of the three plants you have in New York, or amp their emissions to where Environmental regulations are violated.

(The answer is rather simple) buy the power locally, and offer the offset of the ancillaries to the counterparty in order for them to serve your load to the local grid, take the power you normally bring in for local energy comissions, and serve the special orders.

your profit stays acceptable to federal oversight and standard market practices, all the while making sure you don't burn anymore fuel than the Dept of Energy will allow (which was an unseen cost in this equation, at first glance), and your emissions credits with the EPA are not compromised.

And so, of the 390 participants in that market, who is available for that daily scheduling, and which is most cost effective? (The answer is generally the person who owes you the most through net total and interest, as this will just offset the month end reconciliation you recieve from them at the end of the month, aside from daily accruals.)
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So, in the case of the Midwest, this would be anyone who has purchased actual plant level assets from the company on installment, and in the case of multiple purchases outstanding the one with the lowest interest rate or highest balance, accordingly.

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i.e. if you need a ride from someone in order to get to work. call the guy who still owes you for the car you sold him, that he is paying off in installments, and offest the vehicle price by the gas money he would normally ask you for. that works better than paying him for the gas, and still waiting for full payment on the car.

but then someone really has to ask "is it really cheaper in terms of cost effect to schedule them all with third-parties?" and at that point, you have to evaluate each of the 183 schedulings, with and without any or all of the rest, and evaluate the variances due to at least three conflicting weather conditions and other process indicators. and they want the answer from you in 45 minutes...

Omnia est Sum,
Ch

BTW: in a world of 100 people, not a damn one of them could be a Sr energy settlement coordinator...

#12

Oh, it would be easier saying "correction 32! = 32*31*32..."

but dont bother in a world of 100 people all the energy we'll use is for 99 electric chair executions.

#13

math nerds.

#14

Ayhja's chess problem would be a lot easier if u consider that any black square is indistinguishible from any other black square. same consideration goes with the white squares. having said that, u would actually come up with a much lower answer.

#15

In my university exams they put with big words on the blackboard: "understanding is part of the test"

#16

my last post considered that a chess board is a chess board, meaning no distinguishing marks on the squares and that there is a definite starting point.

but for arguments sake, let's just say its an 8 x 8 matrix consisting of numbered squares or even different colored squares.

let's say all these squares were put in a box and that u could pick any one randomly. let's start off at a corner. u'll have 1/64 chances in picking the right one. the next pick would have a 1/63 chance in being the right one. ...and so on.

but there are 4 corners in an 8 x 8 matrix so u'll actually have a 4/64 chance in picking a corner square and u can start from there.

this is the tricky part, the problem does not stipulate whether the next square is to be placed to the left, right, up, down, diagonally, after two squares, etc. it doesn't even stipulate that u have to start at a corner. u can in fact argue that u can start anywhere. therefore any square picked is the right one.

following that argument, any subsequent square picked will be the right one. just place it where its supposed to be. again, there is no stipulation on where any subsequent square is to be placed.

therefore, the answer is ONE !

#17

I can honestly say, that probably for the first time ever, I feel very much outclassed in VU..! Even when raum is discussing lofty, esoteric ideas, I can at least follow them...

Math blows me out of the fucking water tho, I'm am no quick thinker when it comes to it...Pity too, because math is my favorite subject, but not my best...

Continue on..!

#18

Ty, it's not math. you can solve it with math, but it is simple process of elimination.

you got 64 squares, 32 white and 32 black. Worst scenario, you have to try all 32 the first time, then, the remaing 31, then the remaining 30,.. and so on for each color. eventually you will only have one square left and one space left.

This means you can add the integers from 1 to 32, and figure out how many tries you have for each color.

this is a factorial of 32 plus a factorial of 32. So add all the numbers from 1 to 32 together, asnd multiply by two.

the sum of the integers 1 through 32 can be expressed as 32! this is called "Thirty-Two Bang", or in crazy math computer lingo "Squeak Thirty-Two"** but regardless it is "The Factorial of Thirty-Two" as far as your math education.

Squeak thirty two is because the exclamation symbol used to indicate factorials makes it seem like someone is emphatically calling out THIRTEEEEE TWOOOOO!" but Mouse (her real name is Colleen) and Otter (real name is prolly Otter, she's weird like that) decided this should be expressed as a "squeak" more than a "yell."

and who am I to deny a pretty girl or two a chance to squeak? /wink.gif" style="vertical-align:middle" emoid=";)" border="0" alt="wink.gif" />
but as far as where they got it, dunno.

and the first step to really getting it is to know Fapper's answer make no damn sense...

/blink.gif" style="vertical-align:middle" emoid=":blink:" border="0" alt="blink.gif" /> Fap, who does your taxes?

#19

Raum, I donno what you mean

but in maths 32! wich i assume is 32 factorial that is 32*31*30*29*28* ... *3*2*1

http://en.wikipedia.org/wiki/Factorial

this is what i relpied
"you pick a random first piece (this number must be multiplied by 64), so the next should only be a white or a black (so you multiply by 32 since you have 32 pieces left of the other colour), then (by 31 since you retired the first piece of the other colour in the first place), then (31), then (30), then (30) ..."

and this is the result i said that can be wrong perhups
"Solution = 64*32*31*31*30*30*....*2*2*1*1"

correcting your first answer 32! * 2 (with 32! not 568 but 32*31*30*...)
the diference we have beetween our answers is that i say

Mine = 64*32*31*31.... -> 2*32*32*31*31 ... -> 2*32!*32!
Yours = 32!*2

now why the hell i multiply all those numbers?
because i start with one choice beetween 64 possibilites so my initial combinations are 64, then i choose one out of 32 so i've got the 64 posibilities and for one of these i have 32 new porbabilities so the global number now is 64*32, on the next step i have 31 so 64*32*31, and so on.

#20

Fap, you are correct in one thing, Factorial is not the correct word. I used to wrong term.

i am look for the sum of ADDING ALL THOSE NUMBERS, not MULTIPLYING.

and i can't be bothered to look the term up, so it is the sum of all integers, 1 to 32.