unreality

If Panther comes back, he's welcome to re-take his spot as long as he's sure that he can be active. It's no problem if he can't, CL is willing to be his permanent replacement edit: round 15 PMs have about 23ish hours to be PMed

haha @ the woman one. Reminds me of a sexist joke I heard...

Haha, I love Cyanide and Happiness ;D

Mumbles, this is the diagram: You picked Goat A originally * a door is opened, Goat B is revealed ** Switch: You get a Car ** Don't Switch: You get Goat A You picked Goat B originally * a door is opened, Goat A is revealed ** Switch: You get a Car ** Don't Switch: You get Goat B You picked the Car originally * a door is opened, and a goat is revealed ** Switch: You get the other goat ** Don't Switch: You get the Car This is the same diagram you made, I think, but you looked at it incorrectly after you made it... Look at the three "Don't Switch" options. Two result in "Goat" and one in "Car" Look at the three "Switch" options. Two result in "Car" and one in "Goat" If you don't switch, you have a 1/3 chance of getting a car If you do switch, you have a 2/3 chance of getting a car

~~~ Round Fourteen ~~~ Dawh X: Cherry Lane Y_Z: dawh Z: dawh CL X: DMS Y_Z: Cherry Lane Z: Cherry Lane DMS X: Dawh Y_X: Dawh Z: DMS Dawh +2, Dawh -1 : net +1 CL +2, CL -2 : net 0 DMS +1, DMS -1 : net 0 Duel Master: Unreality 1) Dawh/Frost - 10 2) CL/Panther - 6 3) DMS - 7

She PMed, so Panther has officially been replaced by CL Sorry Panther, but inactive twice in a row, especially in the final stages of the game when there's only three people total, can't be left that way. With three people left, three people should be casting spells Anyway, Round 14 coming up!

Yes, that's correct.... which is why it's strange that it's going over. Maybe that's not the convergent? Maybe it doesn't converge at all? It might "make sense" but I'm not sure if the overall formula would be that simple... hmmm...

This is the second time in a row... so I'd say yes. It's now a race ;D Whoever PMs me with Panther's moves first (CL or Panther) will become the new Panther

Guilty on both accounts

Well Dawh and DMS PMed, but Panther has forgotten, again I'll give it an hour tops, then Round Fourteen will happen without him

so did you solve it?

Thanks for doing that!!! It's got to converge to 3.219... (log base 2 of 10). What else would it be doing? At 80 million iterations it's pretty much there. It must have gone over somehow? But the log's convergence so far doesn't jump over and below, over and below, etc, logarithms don't do that and all of our tests seem to follow the pattern of approaching slowly from below... yet it's gone over? Is the limit possibly infinity, just very slowly? I'm so confused now But 3.22 is so close that it's tantalizing, even if it's over ;D the question is, why? I'm trying to think of a way to turn that equation in post 5 into some sort of recursive pattern using the properties of logarithms, but no luck so far

Waah all these Mafia games are so tempting, I want to jump back in But I just don't have the time, especially for the turbo-speed versions that seem to be popular lately

Yeah it was a good plan to try to save yourself, unfortunately it backfired.... thanks for playing though! That may be useful in the, er, little surprise that will happen in the final seconds of the Mage Duel [remember all of this is happening in a few intense-action-packed minutes of nonstop spellcasting in the Duel Chamber]

~~~ Round Thirteen ~~~ Dawh Freeze: DMS Shield: CL Curse: DMS Coup de Grace: Panther Flummox: Panther Vacuum: Panther Spell of Choice: QPQ I Cherry Lane * Freeze * Shield - dawh * Curse - panther * Coup de Grace - panther * Flummox - panther * Vacuum - dms172 * Aqua Vida Panther [?] dms172 * Freeze - Dawh * Shield - panther * Curse - CL * Coup de Grace - CL * Flummox -Dawh * Vacuum -Dawh * Aqua Excessum * No Vacuums and only one Flummox succeeded- Dawh's Flummox. However he cast that on Panther, who didn't PM, thus it has no real effect * Nobody paralyzed * Shields and Curses: Duel Master: Unreality 1) Dawh - 9 2) CL - 1 3) Panther - 6 4) DMS - 7 * Dawh's QPQ I: Duel Master: Unreality 1) Dawh - 9 2) CL - 2 3) Panther - 6 4) DMS - 7 * then the Aqua Vida/Excessum combo applies, and CL gets -2 and drops to 0 Duel Master: Unreality 1) Dawh - 9 2) CL - 0 3) Panther - 6 4) DMS - 7 Due to DMS's Coup de Grace, Cherry Lane dies! Goodbye CL! Duel Master: Unreality 1) Dawh - 9 2) CL - DEAD 3) Panther - 6 4) DMS - 7 It was fun while it lasted... your death marks an important event, however: the transition into the Final Duel! Duel Master: Unreality 1) Dawh - 9 2) Panther - 6 3) DMS - 7 With only three people left, the rules are changing considerably! 1) there is no such thing as Freeze, Shield, Flummox or Vacuum. Coup de Grace will be gone as well because with only three people, it's basically unneeded. Thus, at the end of each turn, anyone with 0 SP will die 2) so the remaining spells are Curse and Spell of Choice... right? Wrong! If it were down to just Curse, the game would be very predictable. In fact, because both are undergoing changes, I'll just say that every single spell as you know it is gone 3) in their place is three new spells: X, Y and Z * X is an offensive spell * Y is a modifier spell * Z is a defensive spell - For each spell, you select one target; this person can be anyone (including you) - The amount of SP loss someone suffers equals X-Z, or the number of X spells cast on them minus the number of Z spells. Thus if they receive more Z than X, they "lose negative", and would actually gain some - In addition, each person loses 1 SP every round - Y modifies someone's spells such that their effect is doubled. You either do Y_X (the strength of the target's X spell is doubled), Y_Z (the strength of the target's Z spell is doubled), or Y_Y (the person's Y spell quadruples instead of doubles). If you do Y_Y on yourself, it's pretty much pointless of course So someone's roster would be like this: Unreality X: Your Mom Y_Z: Unreality Z: Unreality or maybe: Unreality X: Jack Shepard Y_X: John Locke Z: Cherry Lane or whatever The final stages of the Mage Duel have begun! Only an intense combination of strategy, skill, alliance and determination can win you the game! so ze roster is: Duel Master: Unreality 1) Dawh - 9 2) Panther - 6 3) DMS - 7

Well it's already 2.5-3ish hours past the 'deadline' (), sorry Panther edit: Actually, it's dinner time. After dinner, if I can get on, Round 13 results will be arriving

I'm adding two problems These ones are as old as Archimedes (5) Two cylinders of unit radius intersect at 90° ... what is the volume common to both cylinders? (6) Much harder, what is the volume common to THREE intersection cylinders? (all at 90°). You'll probably need calculus for this one...

Since Prison Break wasn't on (damn baseball! ), I actually got to watch Heroes again! It was pretty cool... the look on Nathan's face when his mom told him that a doctor gave him his powers, not God Score one for atheism ;D hehe jk, jk

Okay, everyone except Panther has PMed me for Round 13... I'll wait a bit more for him

I agree Prime We know that base2 is the best, we haven't said differently. And we're talking about purely mathematical digit storage here, not speed or anything else ;D

#0 is like a Practice Problem, the rest are actually a bit harder (0) Take any number. Now take the square root and add 2. Do this repeatedly. What happens (no matter what you number you start with), and why? (1) What is the value for n that gives the highest result for the nth root of n? (2) If you pick numbers randomly from 0 to 1 (inclusive), how many picks would you expect [on average] it would take you for the total sum of the numbers you've drawn to reach or pass 1? (3) Given the defining property of the Golden Ratio: p2 = p + 1 Prove this formula: pn = F(n)*p + F(n-1) and this one: pn = pn-1 + pn-2 Note that p has the quadratic equation: p2 - p - 1 = 0 thus the values are (1+√5)/2 and (1-√5)/2, and both have the properties of p F(n) = Fibonacci number Fibonaccis: add the previous two: 1,1,2,3,5,8,13,21,34,55,89,etc ie, F(7) = 13 also, negative Fibonaccis hold up to the rule that the previous two add to the next one, so a full box might be: n: -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 F(n): -13 8 -5 3 -2 1 -1 0 1 1 2 3 5 8 13 [/codebox] (4) extra credit for number 3: Can you create a formula based on p & n which calculates F(n) without using any other F(x) in the equation?

Sounds good Let me know how it turns out

Cuz I had no rule as to what would happen with multiple Aqua Vidas/Excessums, and I had three different possible routes: 1) they work in pairs of cancellation, with leftover Aqua Vidas adding +2 as usual and leftover Aqua Excessums having no effect 2) the number of Aquas cast doesn't matter. Either there is no Aqua spells cast (no effect), or there is all Aqua Vidas with no Excessums (this is +2), or all Aqua Excessums with no Vidas (no effect), or a mixture of both (in this case, Aqua Excessum pollutes Aqua Vida and turns +2 into -2) 3) the number of Aqua Excessums is diluted by the number of Aqua Vidas and this effects the SP loss It would be unfair NOW for me to arbritarily decide which one is the correct one when your life is on the line. Thus I rolled randomly And since I rolled option #1, that will be the case from now on. The Vida/Excessum spells work in cancellation pairs

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