That One Thread

[Parrhesia]

Oh, he's very intelligent, alright. But just not used to the keyboard. Hence, grammar issues.

He whined about trolling.

Tell him what trolling means. Then introduce the saying "People who live in glass houses shouldn't throw stones."

[AstraLunaSol]

I'm gonna try to explain this as simply as possible.

The redlines below his head are his neck, and where they shooouldish be.

The redlines near/overlapping the border of his hair are better more natural looking lines.

The lines inside of the hair are suggestions to make it more "curvy" Since your hair shaping is pretty irregular, when you're making the bangs and hair shape, you have to have them at points. And the 3rd shade should be the color that makes the basic shapes.

Edited December 23, 2010 by Utatane Piko

[Thor Odinson]

Alright. Thanks man. :3

*goes to fix*

[Parrhesia]

FE5 mugs are beautiful. PoRD are my favourite though. But I like GBA, FE5 and DS equally.

My mind switched off. I meant to say THAT FUCKING SETY IS BEAUTIFUL. ...But yeah, the last two sentences are legit.

[Nanami Touko]

Oh, he's very intelligent, alright. But just not used to the keyboard. Hence, grammar issues.

Uh...

Furet trolls him with threats of Shotgun castration, and he retorts with "i can beat you in a fist fight"

THE PINNACLE OF INTELLIGENCE!

[Thor Odinson]

My mind switched off. I meant to say THAT FUCKING SETY IS BEAUTIFUL. ...But yeah, the last two sentences are legit.

Thanks Furet~

[Kriemhild]

FE5 mugs are beautiful. PoRD are my favourite though. But I like GBA, FE5 and DS equally.

FE5 Sety looks awesome. And <3 Rinehart.

From your university, Proto? :3

Smogon University, actually, which is a website on Competitive Pokemon. In other words, another forum.

PoRD is pretty much legit full-scale artwork.

And PoRD has DAMN GOOD artwork.

Yes, they look really good. I really want to see Rinehart or Shannan in that artwork...

He whined about trolling.

Tell him what trolling means. Then introduce the saying "People who live in glass houses shouldn't throw stones."

Alrighty.

[Nanami Touko]

SPEAKING of FE5. Kempf. Kempf is a magnificent bastard.

[Nanami Touko]

And, thus marks the end of anything I do to this Ayra sprite. Dan, I made the head+hair one pixel higher. Sitting at 47, I think it looks fine. Heck, Amera's head+hair is only 46, and it looks fine the way it is. I think your 50-52 pixels high is a bit much .__.

[Thor Odinson]

It's just the nose now. Everything else looks fine to me.

[Thor Odinson]

Astra

better Y/N?

[Kriemhild]

Buckministerfullerene

Also, I'm posting this link for the sole purpose of preserving it:

[spoiler=Math][spoiler=Two Integers]Meanwhile, here's a tougher problem. At the end of camp a couple of years ago, we were given a problem of the year. I solved it in a day, and I found out next year to my surprise that I was the only was to email in the solution. I learned a few months later that this is a famous problem, so don't spoil the answer if you already know it. Anyway:

A teacher announces to her students, "I have picked to integers a and b that are both greater than 1. I will tell Rod their product and Sue their sum."

After the teacher gives the two students, who are both perfect mathematicians, the information, they have this conversation:

Rod: I do not know the values of a and b.

Sue: I already knew that.

Rod: I now know the values of a and b.

Sue: I now also know the values of a and b.

What are the values of a and b

[spoiler=Goat problem]A goat is tied to the corner of the outside of a barn by a rope 12 meters long. The barn is rectangular (or a cuboid if you want to be pedantic but only 2 dimensions matter) with sides of length 6 meters and 4 meters. Assuming that the area around the goat is free of obstructions asides from the barn, that the barn is shut and any other weirdness you want to throw in to make the question easier, what area can the goat roam in?

133π-12+12sqrt(3)-(64π(arccos((6sqrt(3)+15)/26))+36π(arccos((6sqrt(3)+2)/13)))/360°

[spoiler=Roads connecting 4 cities]Four cities are located on the corners of a square, 100 miles along each side. The cities need to be connected by roads, but they don't need to be connected directly, they can just meet at a midpoint if you want. You have a budget of £275 million and each mile of road costs £1 million, regardless of location. Is it possible to connect the cities in your budget, and if so how much will you spend at a minimum?

http://img651.imageshack.us/img651/1360/roadproblem.jpg

[spoiler=Red/green hats]In a certain town, everyone wears either a red hat or a green hat. Every morning, each person sees everyone else in the town. Each person can see everyone else's hat, but no one dares to look at their own hat because if one discovers that his or her hat his green, he must kill himsef that night. Since the beginning of the town's history, no one killed himself, but one day, a stranger comes to the town. He says out loud, in a voice so loud that everyone in the town can hear him, that everyone in the town wears a red hat or a green hat. Then he leaves immediately. What happens?

everyone who has a green hat kills themselves on the nth night, where n is the number of people wearing a green hat.[/color]

[spoiler=Pills]You wake up feeling sick one morning, so you go to doctor. He tells you that the illness you have is normally terminal, and most people with it die (what's with these bloody questions?). But there is a cure. He gives you two bottles: one labeled A and one labeled B. Each contain 15 pills. For the next 15 mornings, you will have to consume exactly one A pill and exactly one B pill. If in one morning you eat more or less than that, you will immediately die. Also, the A and B pills are identical and completely indistiguishable, even by the doctor himself. Finally, there are no others A or B pills in the entire world (hey, some people don't believe in coincidences, and this is one of those cases).

So the next morning you follow your instructions and eat one of each pill. The next morning, however, you accidentally pour one A pill and two B pills into your hand, and you don't know which is which. What do you do?

[spoiler=Chain rings]You find 5 chains. 2 of them have 3 rings, and 3 of them have 4 rings. You take them to the blacksmith to make one long chain. It costs 10 cents a cut and 10 cents a weld. Each cut only cuts one ring (so no stacking) and each weld only welds one ring as well. What is the cheapest way to make the chain?

60c

[spoiler=Wolves and Sheep]I'm not sure how hard this really is, but you have a 5x5 chessboard. On this chessboard you must place 5 wolves and 3 sheep. A wolf moves like a queen in chess (vertically, horizontally, or diagonally), and none of the sheep can be in the attack range of the wolves. Where are all of the animals placed?

O O d d d
d d d X X
d d d d X
O d d d d
d d X X d

[spoiler=Buckets of water]One holds 8 litres, one holds 5 litres and one holds 3 litres. My 8 litre bucket is full, but I need to get 4 litres from them today. How can I do it?

[spoiler=Add lines]11 = 113355

Add four straight lines to make this an equality (no, crossing out the equals sign does not count)

Too easy?

Do it with 3 lines. It doesn't have to be exact, but must be accurate to at least 7 significant figures

[spoiler=Two discs in a box]There is a box, 9cm by 10cm. Inside there are two discs which fit exactly (each disk touches two sides, so they're in the corners) and touch at P. Radius of Disc A is 4cm, centred at A, and Radius of Disc B is x cm, centred at B. 3(5 - 2(5^0.5))

[spoiler=Two circles]What is the area of intersection of two unit circles, given that the center of each circle lies on the other circle?

[spoiler=Connect all dots]...

...

...

4 lines, no picking up the pencil. Too easy?

....

....

....

....

Go through all dots with 6 lines without picking up your pencil. There are many solutions, so find one with at least 2 lines of symmetry and some sort of rotational symmetry.

[spoiler=Semicircles in a quartercirlce+triangles with the same base]

1. What is the ratio of the blue area to the red area? The shape is made of two semicircles and one quarter circle. 1:1

2: Find x. The bottom left angles are equal, and the bottom right angles are equal.π/3

[spoiler=Polynomial Series]A sequence of polynomials a_n(x) are definsed recursively by

a₀(x) = 1

a₁(x) = x² + x + 1

a_n(x) = (xⁿ + 1)a_n-1(x)-a_n-2(x), for all n > 1

For example,

a₂(x) = (x²+1)(x²+x+1)-1=x⁴+x³+2x²+x

a₃(x) = (x³+1)(x⁴+x³+2x²+x)-(x²+x+1)

= x⁷+x⁶+2x⁵+2x⁴+x³+x²-a

Evaluate a₂₀₁₀(1).

4021

[spoiler=9th Degree polynomial]The polynomial p(x) is of degree 9 and p(x) − 1 is exactly divisible by (x − 1)⁵.

(i) Find the value of p(1).

(ii) Show that p'(x) is exactly divisible by (x − 1)⁴.

(iii) Given also that p(x) + 1 is exactly divisible by (x + 1)⁵, find p(x).

[spoiler=1 to 200 in two anti-parallel groups]The numbers 1, 2, 3, ..., 199, 200 are partitioned into 2 groups of 100 each, and the numbers in one group are arranged in ascending order: a₁ < a₂ < a₃ < ... <a₁₀₀, and those in the other group are arranged in descending order: b₁ > b₂ > b₃ > ... > b₉₉ > b₁₀₀. Find the value of the expression

|a₁ - b₁| + |a₂-b₂| + ... + |a₉₉ - b₉₉| + |a₁₀₀ - b₁₀₀|

[spoiler=Sum of digits in Death]Consider a function S(x) that takes an integer x and displays the sum of the digits of x. That is, S(103) = 4, and S(S(47)) = S(11) = 2. Find the value of S(S(S(44444444))). A word of advice - don't try to calculate that number.

S(S(S(x)))... it bears similarities to multiples of 9, that's clear. But how does that help? Well... S^∞(x) ~= x mod 9, I believe, or at least is correct when 9|x. This also has similarities to multiples of 3, for identical reasons.

So S(S(S(x²))) will do the same thing, but with x². Duh. But how does the value of them compare? I have no idea. I'm going to call S(S(S(x))), f(x), because it's boring to type out <img src='http://serenesforest.net/forums/public/style_emoticons/<#EMO_DIR#>/biggrin.gif' class='bbc_emoticon' alt=':D' />.

In increasing x:

.........1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20
f(x) = ..1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2
f(x^2) = 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4

Even if you can't see why, it should be clear that there's a pattern there that repeats every 9 digits.

Anyway, let's expand that one more...

.........1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20
f(x) = ..1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2
f(x^2) = 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4
f(x^3) = 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8, 9, 1, 8

Now we're getting somewhere. It seems that, at least for sufficiently small x (and sufficiently small can get pretty large, I think - even for y ~= 10^10,000, S(y) ~= 50,000, S(S(y) could be from about 1 to 40, S(S(S(y) is likely single digit). 4444 mod 9 = 7, so I'll focus on what happens to the mod 7 numbers in this table (7 or 16, both hopefully will be identical):

f(7^1) = 7

f(7^2) = 4

f(7^3) = 1

f(7^4) = 7

f(7^5) = 4

f(7^6) = 1

f(7^7) = 7

f(7^8) = 4

f(7^9) = 1

A pattern appears obvious. I've done no proving, but since 4444 mod 3 = 1 (i.e. 1 more than a multiple of 7), it seems fair to say the answer is 7.

If you want proving, I can attempt to verify my assumption, but I make no promises I can.

[spoiler=24 balls, 4 colors game]A game has 24 balls: six in each of four different colours. One ball of each colour contains a slip of paper saying win, while the other five are empty. You may play the game once for 20p, or six times for £1 (100p = £1). If you play six times, then you choose a ball, it is opened, you see if you won or not, that ball is not replaced, and then you choose the next ball. For each winning ball you open, you win 50p

a: What is the chance of winning when playing a single game, and what is the expected earning (or loss)? 1/6, 11.67p loss

b: Assuming the best strategy* is played, what is the chance of getting 0, 1, 2, 3 and 4 winning balls from the £1 game? Therefore, what is the expected earning? 5/432, 23.958333333p loss

*This isn't too hard to determine, but you have to work out what it is

[spoiler=Rockets probability]Satellites are launched using two different types of rocket: the Andover and the Basingstoke. The Andover has four engines and the Basingstoke has six. Each engine has a probability p of failing during any given launch. After the launch, the rockets are retrieved and repaired by replacing some or all of the engines. The cost of replacing each engine is K.For the Andover, if more than one engine fails, all four engines are replaced. Otherwise, only the failed engine (if there is one) is replaced.

a: Show that the expected repair cost for a single launch using the Andover is

4Kp(1 + q + q2 − 2q3) (*)

Note: (q = 1 − p)

For the Basingstoke, if more than two engines fail, all six engines are replaced. Otherwise only the failed engines (if there are any) are replaced.

b: Find, in a form similar to (*), the expected repair cost for a single launch using the Basingstoke.

c: Find the values of p for which the expected repair cost for the Andover is 2/3 of the expected repair cost for the Basingstoke.

[spoiler=Colored balls in an urn]Consider an urn containing 6 white balls, 7 blue balls, and 10 red balls. What is the probability that three balls chosen at random are all of the same color. Assume that they are all equally likely to be drawn, and that selection is done without replacement

75/733

[spoiler=Cross the Bridge]4 people need to cross a thin bridge one night. Only two people can cross it an once, and since it's dark, the flashlight needs to be with any person or pair crossing the bridge. One of them can travel across the bridge in 1 minute, one can travel across it in 2 minutes, one can travel across it in 5 minutes, and one can travel across it 10 minutes. If two are going across it an once, they will travel at the slower speed. What is the fastest way for everyone to cross the bridge?

17 minutes

[spoiler=THEY ARE INTEGERS!]x² + y² + z² = 2(yz + 1)

x + y + z = 4020

Find all possible values of x, y and z

[spoiler=Show some stuff from some algebraic equations]x, y, z and a are non-zero real numbers which satisfy:

2a - 3y = (x - z)²/y

2a - 3z = (y - x)²/z

Given that y ≠ z, show that a = x + y + z and that a²/2 = x² + y² + z². Are these equations still true if y = z?

[spoiler=Probability questions with die]Which is more likely: That I roll a double 6 with two dice at least once in 100 rolls, or that I roll a quadruple 6 with 4 dice at least once in 3,600 rolls? Double 6 in 100

I have 5 dice: one is biased and always rolls a 6, the other 4 are unbiased. I pick two at random and roll them, and get a double 6. I roll them again. What is the probability that I get a double six again? 5/36

[spoiler=Heart with Area Perimeter]A heart is constructed from two semi-circles and an equilateral triangle, as shown in the diagram above. The area of the heart is x cm2, and the perimeter of the heart is also x cm. What is the exact radius of the semi-circles in the diagram?

r=(2π²+16π+32)/(π²+(4+4sqrt3)π+16sqrt3)

[spoiler=An exam about the exam]Isaac attempts all six questions on a BMO paper. On each question, he gets a score between 0 and 10 inclusive (so 0's and 10's are possible). Given that he never scores more highly on a later question than an earlier question, how many different combinations of scores can he achieve?

8008

[spoiler=Square function]Consider a function f(x,y) such that for every four points that form a square, the sum of the values of f(x,y) at those points = 0.

It is quite obvious that the solution f(x,y) = 0 is a trivial solution to this problem. Your question is this: Are there any other functions of two variables that can satisfy this condition? If so, provide an example. If not, prove that there are no other functions that do so.

You have ten trees. Line them up in such a way that you have 5 rows of 4 trees each. *a star*

How many ways can you make exactly £10 using only 5p, 10p and 20p pieces? 2601

How many four digit numbers are there that are divisible by 9 and comprise of four different odd digits? 24

How many four digit numbers are there that are divisible by 9 and comprise of any four odd digits? 81

Edited June 23, 2014 by Railgun

[Parrhesia]

FURET'S LIST OF PEOPLE WHO WOULD TURN HIM GAY

*=Fictional

GABRIEL BYRNE

LEGAULT*

GABRIEL BYRNE

GABRIEL BYRNE

LEGAULT BEING PLAYED BY GABRIEL BYRNE (a possibility!)

Hmm...a little out of date now. *rubs off the dust and adds*

SETY

*Looks critically at it, then adds*

SETY PLAYED BY GABRIEL BYRNE

LEGAULT AS PLAYED BY GABRIEL BYRNE DISGUISED AS SETY

[Thor Odinson]

That's quite a list.

[Kriemhild]

Sety I can understand. Legault I do not.

[Altera the Hun]

Legault is awesome. Especially while he's harassing Heath.

[Nanami Touko]

So, I stuck it up next to Dan's Tiltyu, and the eyes/nose/mouth were one pixel too low.

I moved them all up, and now I am stuck as to how to make it better.

[Thor Odinson]

I feel it's more of the shape of the nose, though.

Also, the only person I'd be Lesbian for is Lucius.

.

.

.

[Psych]

OH MY GOD, DID I REALLY JUST PICK ASTRID

[Parrhesia]

The nose is, I think, a little too far over to (our POV) left. Move it over by a pixel or two?

[Altera the Hun]

I feel it's more of the shape of the nose, though.

Also, the only person I'd be Lesbian for is Lucius.

.

.

.

Whatever happened to that thing with Lakche? >.>;;

[Nanami Touko]

I feel it's more of the shape of the nose, though.

Also, the only person I'd be Lesbian for is Lucius.

.

.

.

You'd be lesbian for ERL? Ewwwwwww.

If you want a manly Japanese man singing about diving through time and firing a Metal Genocider, look no further.

[AstraLunaSol]

And, thus marks the end of anything I do to this Ayra sprite. Dan, I made the head+hair one pixel higher. Sitting at 47, I think it looks fine. Heck, Amera's head+hair is only 46, and it looks fine the way it is. I think your 50-52 pixels high is a bit much .__.

Compare to the Lakche.

Astra

better Y/N?

much better

[Nanami Touko]

The nose is, I think, a little too far over to (our POV) left. Move it over by a pixel or two?

I tried it. It really didn't work. Thanks anyway, Furet.

[AstraLunaSol]

The nose needs to be pointer. That's what.