talk to the face cos the hand ain't listening

2005-08-14T05:29:00.000-07:00

this weekend is r weekend. all abt r. (: (: :D

how come?

because <3<3<3

2005-07-11T07:41:00.000-07:00

today, the thoughts have been going boing boing in my head.. those bouncy thoughts. but for once in the longest time, they were happy thoughts.

weekend was... wow. and i would jus laugh, because there's no other way i know to express the way i feel.

you made it special.

2005-07-01T08:13:00.000-07:00

OMG I SO NEED TO DRIVE. I would burn my tires out for all they're worth.

then in the boot i can put my blades and my beloved basketball. (:

2005-06-23T11:49:00.000-07:00

and it was beautiful.

2005-06-22T06:57:00.000-07:00

heat and sweat kills the desire to do anything. even nuahing becomes annoying. and stupid reception was like, bad. i got to see those vultures though at around 5pm. or some big birds flying abt circling. and that chinook landing would jus blow every piece of dirt on the ground onto my body.. like bullets gosh.

it's been 2 days. yes 2 days. finally. it's like going home to ice cream after baking in the sun. which unfortunately did not happen to me today. but KFC was good enough.

my thoughts for tmrw were found in the clouds of the sky. and they were beautiful.

2005-06-20T08:33:00.000-07:00

bloody bus. cant believe it broke down twice.

it was a nice walk. i can't believe someone got me to care so much.

2005-06-16T08:03:00.000-07:00

when I was a young boy
I tried to listen
and I wanna feel like that
little white shadows
blink and miss them
part of a system I am

if you ever feel like something's missing
things you never understand
little white shadows
sparkle and glisten
part of a system, a plan

all of this noise, I'm waking up
all of this space I'm taking up
all of this sound that's breaking up
ohhh...

maybe you get what you wanted
maybe you stumbled upon it
everything you ever wanted
in a permanent state

maybe you'll know when you see it
maybe if you say it, you'll mean it
and when you find it, you'll keep it
in a permanent state
a permanent state

when i was a young boy
i tried to listen
don't you wanna feel like that
you're part of the human race
all of the stars in the outer space
part of a system, a plan

all of this noise, I'm waking up
all of the space I'm taking up
I cannot hear, you're breaking up
ohhh...

maybe you get what you wanted
maybe you stumbled upon it
everything you ever wanted
in a permanent state

maybe you'll know when you see it
maybe if you say it, you'll mean it
and when you find it, you'll keep it
in a permanent state
a permanent state

I swear I'm only seeing faces
tired of the human races
oh, an answer now is what i need

see it in a new sun rising
see it breaking on your horizon
oh, come on love, stay with me

-white shadows, Coldplay

Ah beautiful. [:

2005-06-16T06:38:00.000-07:00

HAHAAHAH for the first time in my life i beat someone at reversi with a score of 62-2 muahahaha.. my poor sister.

bloody cover. bloody hot. bloody waste of time. sleep was good though from 8.40 to 9.40. and from 12 to 2. even though it was hot. yes. even though it was bloody hot. and deathnote jus took an irritating turn though.. argh horrible.

2005-06-14T07:00:00.000-07:00

wa lao eleven is a bloody scary number. what a coincidence.
now it's gonna be my favourite prime. and it's the fifth prime some more.
too bad ernest. go settle for thirteen or something. prime freak.

bloody hell my sis got an electric. damn.

i'm definitely gonna learn californication on the electric.

2005-06-13T07:36:00.000-07:00

i got dosed by you
closer than most to you
what am i supposed to do
take it away i never had it anyway
take it away and everything would be ok

in you a star is born
you cut a perfect form
someone forever warm
lay on lay on lay on lay on

way upon the mountain where she dies
all i ever wanted was your life
deep inside the canyon i can hide
all i ever wanted was your life

show love with no remorse
climb onto your seahorse
this ride is right on course
this is the way i wanted it to be with you
this is the way i knew that it would be with you

-dosed, RHCP

2005-06-10T15:44:00.000-07:00

wheeeeeeeeeeee!!! i'm delirious!!!! (: (: (: (: (: (: (: (:

2005-05-31T08:42:00.000-07:00

hate waking up. i'm always confused when i wake up. esp today after my nap. my dream was like jus some action stuff and i wake up confused over other things. irritating.

pool was good today. cleared my mind. always does.

2005-05-30T09:07:00.000-07:00

life is like a DNA strand. or a double helix structure that loops back into itself. so full of apparent vicious cycles that makes u wonder if it leads anywhere. and no one knows what it means.

Z.

yes zonked. eyes heavy, but mind still working. it's like thousands of pinballs bouncing off the sides of my intercerebral membrane. -doing doing- if what we conceive in our thoughts cannot be appreciated by people, does that make it worthless?

i want to make this perfect.

ok i'm yawning.

2005-05-30T05:37:00.000-07:00

ah the silly love songs.

i've completed chapter one!!!! muahahaha!!! finally.

talking abt the golden ratio and fibonacci numbers with my doctor was cool. it's like everybody associates math people with fibonacci numbers. and have no idea what those numbers really mean. but it didn't even take him like 2 seconds to discover i was bloody blur. heh heh.

cup noodles and fries for supper today sure made me a happy man. ;)

think i'll go back to my music and art.

2005-05-27T21:03:00.000-07:00

I Am Insane.... And You Are My Insanity... says:
talking to a gal at the ambulance bay is actualli very nice.. should try it out..

aiyah ramesh ramesh. yes oh so clean.

i lost to slash in MVC and MSHVC. damn i'm losing my touch.

-currently addicted to evanescence- my immortal is SO nice.

2005-05-27T03:09:00.000-07:00

You've been hurt by unspeakable pain and sadness.
Let's carry each other's indelible stains.
Don't give up on living.

I held your hand.

Will I end up losing them someday?
I want to protect you and your fading smile, so
Even if the resounding voice calling me should wither...
Even if the mingling winds should tell me...

I will find you.

You've been hurt by unspeakable pain and sadness, but
Don't say things like "I can't laugh" or "I hate people".
There's meaning in everything that happens in the unseen future.
So stay as you are for now, I know there'll come a time when you realize it.

You and me, two are spoken.

Someday we'll understand each other.

-theme from bleach.

i so love this theme. it's jap, so the weird english translation bothers me but the song and the opening clip is SO hot. Bleach ROCKS!!

2005-05-23T05:16:00.000-07:00

rui - i wanna see the pics!!

curry chicken and stingray and potato/beef and peanut soup. for dinner. i'm treated like a king!
(thanks grandmama)

2005-05-21T10:33:00.000-07:00

i can't do inequalities!!! argh!! the only one i solved used differentiation and induction. which is by no means elegant, though short, but not elegant.

good performance everyone. well done rui though the hair thing.. but still good overall.. nice paranoid sam.. and other pple i do not know.. well interesting overall. albeit having to tahan diarrhoea during the first half, but i succeeded. i almost bought like cemetery flowers. phew. ok u pple i gave flowers to, i didn't say that.

i liked my new black shirt. con-ed my aunt into buying it for me herh herh.. and it's for christmas. HAHAHAHAHAHA

2005-05-18T06:32:00.000-07:00

work is proof for society that u exist.

2005-05-18T05:56:00.000-07:00

robin the witch hunter is DAMN good. So is bleach episode 31. bleach has like my favourite opening, and for all who watches it, it's the second opening. the first one sucked.

while walking a few days ago i was thinking to myself that i should place a list of popular anime stuff on my blog. by that i mean, stuff people always talked abt. it's like u say it, and everybody knows.

and i only thought of one. how a three pointer in slam dunk lasted one whole episode. classic.

rouge is really irritating to draw. i can't draw the face curves right. and sega gave her breasts. did i mention i couldn't draw women for nuts?

food is good. food is good. wanton noodles after fishball noodles or chicken rice is always satisfying no matter how bad the wanton noodles are.

2005-05-08T02:45:00.000-07:00

mommy's day - thank god i had that zinger and nuggets (i lost count) before we went to that jumbo restaurant. seafood is so not my thing. and did u know seafood chicken can taste bad? i had my cousins thinking that chicken was a seafood. well only for 3 seconds. and they like, young. ooh.. what an achievement for me! i think i'm gonna slam the door on my finger so i seem less stupid.

oi rui hope u get better. dun dwell too much on it k.. not good for yer. and so sorry i pissed u off. dun take the things i say too seriously yea? let's go chill! (shucks i was never good at consoling pple. i've been like so close to depressed pple, and still never really got the hang of it. sigh.)

i'm so happy i'm closed to finishing to chapter 5. of my comic. i really like the last pic where shadow like sits up from the bed.. cos it's really big muahaha

off to draw. inspiration's here again. hi there inspiration.

(jus slam it on my finger. quick.)

2005-05-07T05:55:00.000-07:00

now another portion of my Sonic script.

i wish the alliteration was intended

cream sees shadow on the beach and shadow is unconscious. in his mind he has visions. ok that's jus exaggeration. he's having a dream. if that's more accurate than a flash back that is.

it's black. shadow finds himself in the capsule that held him while he was being engineered in the ark. questions fill his head like some sort of incessant screensaver.

Shadow: where am i, what am i doing here, blah blah (i dun really want to type this cos i already drew this. the rest i haven't)

two figures appear. Dr Gerald Robotnik (Eggman's Grandfather) and this GUN agent. i call this agent X cos he doesn't have a name yet.

X: Doctor, your research is too slow. We need weapons and we need it fast.

Gerald: yes i know that, i truly apologise, but-

X: we have decided to withdraw our funding of your research soon. the high echelons are very upset at the standstill you've reached.

Gerald: no u can't! not now. not now. when i'm so close to saving her. so close..

Shadow: Gerald? Doctor?

(next panel)

X: i empathise with u, but u must understand that we cannot sacrfice all our money for pity's sake.

Gerald: u can't..

X: we are an organization. there are some things we must do-

Gerald: u can't... she's my grand-daughter.

(next panel)

Shadow: Maria? Where are u? Are u safe?

X: I'm sorry.

(next panel - gerald alone)

Gerald: Why? why do they see u as a weapon? u're not. u're so much more than that. u have "it". i know. because i gave it to u. u... u.. are my only hope..

Shadow: hope? hope? hope...

(next panel - blank)
Gerald: AAAAAAAAAAAAAARRRGHH!!

(next panel - gerald again)
Gerald: i've lost everything. EVERYTHING! she died.. she died..

Shadow: maria? maria died!? doctor doctor! ANSWER ME-

Gerald: all i've ever worked for. so that she could live.. so that she could live..

Shadow: it can't be.

Gerald: no it's all their fault. they will answer for it. they will. they will face my ultimate weapon. they will face MY WRATH! MY VENGENCE! i will have my revenge.. i will..

(change panel - maria)

Maria: Shadow.. shadow.. u have got to go. it's dangerous here. pls go. pls. dun worry abt me. i will always treasure the time we've had together.

Shadow: no maria, dont!

Maria: promise me. promise me.

(change panel - maria)

Maria: bring hope to humanity.

(suddenly mecha sonic's cloak covers her.)

Shadow: NOO!! MARIA!! This can't be happening!!

Mecha Sonic: weak.

Mecha Sonic blasts the capsule. Shadow wakes up with a cry.

(end)

damn my stomach. i can calculate the increasing d2y/dx2 of the curvature of my tummy. and that's not v nice.

2005-05-03T07:59:00.000-07:00

i still have eight entries also. if only having a homomorph from the apparent no of entries to the actual no of entries would be monotonic. damn. so much for an isomorph.

today was probably one of the most interesting days in my medical centre since .. urm.. a long time? the new reservis today is a math/stats professor in NUS!! got to talkin abt like math in general, what he does, how a prof's life would be, etc etc. a pity we didn't get to talk abt real math.. seriously if anybody tells me abt math, i'd be darn interested. even if it were stats. the bane of all mathematics. and the most useful besides analysis. doesn't say much though.

today i drew my first cream. cream and cheese.. the dynamic rabbit/chao duo from Sonic Advance 3, Sonic Heroes and the like. but they're too cute. the characters. not my drawings. seriously everytime i draw cute characters it's like coming up with a lame derogatory for their name. Tails was disaster enough already. anybody wants to see how she looks like, go to yahoo, search for Sonic Heroes, and look at the pics! lazy to add the link. oh but the dialogue was strangely apt for my comic today. good that i'm taking more time to think of what my characters would say. Thanks the whole bunch of yer geps for your comments. i know sonic's not the most popular character ard and i appreciate the accomdation. :) bowling was fun. it killed my wrist.

and i can't draw sand. and water. and the beach. damn.

oleanna is a bloody good read. rape? are these not facts!?

two things make my balls shrink.(think of this last line not as a crude saying but a figure of speech.. a literal figure of speech) the smell of hard liquor out of a guy with bad teeth/breath, and puke. puke in a ziplog bag... is STILL puke.

2005-04-21T02:59:00.000-07:00

damn the work's piling. do so much work in the army.. i should get regular pay.. no wonder my seniors were telling me.. dun work so hard.

then again, i tell myself that for everything i do.

in a rather queer manner i find the barking atmosphere rather satisfying. pple make mistakes and pple scold the ones who make mistakes and pple involved blame those who make the mistakes, saying that they wouldn't make those mistakes when they've in fact made worse ones. and another pple gossip.

and i would say, spin my head so i can see my posterior.

consider the event that leads us to where we started. is that a waste of time? and now i see a radiator burst problem. timing is good.

drag me a purple stain and flex my lips.

pool is good. ultimate relaxation. had that last fri with my best frens and itching for more. chia said: it jus seemed like yesterday three of us were eating together in the rosyth canteen. and me and zuzhao said: no. zhan where are u?! soon we'll crash your place and play smash brothers. pichu's my thing man. If u read it in a certain way, it brings abt a very small feeling, can't feel the damage to my ego though. oh, and electrifying.

so i sit. and i wait.

like for so many others.

ponder.

2005-04-13T07:08:00.000-07:00

My blogger site status insists i have only 8 entries. like i didn't know that.

jus to pen down a conversation i need to include in my comic. i realize i can't think of panels to draw and words at the same time.

(Sonic and Mesh in the Sacred Chao temple)
Sonic: so u light up one flame and all the other flames light up as a result. Amazing. Sacred temple indeed.

Mesh: This temple contains even more mysteries that we can imagine. People say that while it reveals much, it opens up many more questions about the world we live in.

Sonic: Intriguing. but dude i gotta ask you. (panel change) what is up with that door?

Mesh: The one we jus came through? Oh well as you already know, the door opens up for thirty seconds only. This happens 3 times a day, sparsed evenly throughout.

Sonic: And that means, being the guardians of this temple, you have to keep it under surveillance esp when the door is open, against like, that Eggman bot we jus faced.

Mesh: Exactly.

Sonic: .. and your chaos energy?

Mesh: ... ... chance. An accident in this temple that made me realized the true destiny of our forbidden tribe.

Sonic: the true destiny?

Mesh: Yes the true destiny. (panel change) We have been guardians of the temple since our tribe has started. More correctly put, in our ancestral ages we were guardians of the sacred chao community that used to live in this temple

Sonic: Sacred Chao? that lived here?

Mesh: yea look. (steps into chao room that looks like Station Square Chao Garden without the water)

Sonic: wow really looks like chao lived here before. jus like in station square.

Mesh: Exactly.

Sonic: wait.. did u say guardians? Boy u sure make it sound as noble as Knuckles makes it sound.

Mesh: Knuckles?

Sonic: Yea the echidna.

Mesh: The echidnas. They're NOTHING like us. (slightly annoyed and furious)

Sonic: ... ...

Mesh: Our ancestral history has it that we once protected the sacred chao because it was said they held the key to the most abundant source of power in the world, the Master Emerald. We couldn't let them fall into the wrong hands because it seemed common knowledge that having them misused was worse than having the Master Emerald misused. In fact, only with them, can the true power of the Master Emerald be used.

Sonic: What's that gotta do with the echidnas?

Mesh: The echidnas were a self righteous race with only their own interests in mind. On the surface they claim to be guardians of the emeralds, but they're actually more like guardians of their possession of the power of the emeralds. (panel changee) A long time ago, the echidnas did not know about the chao, thus they lived peacefully with the world, a sense of kingship attached to them for the knowledge of the emeralds. But once they discovered about chao, they sought to eliminate them all in the excuse that they posed danger to the rest of the world. Rather, it was because of their worry that the chao might overtake them as the honoured ones of the world that they carried out their cruel annihalation.

Sonic: But the echidna race eventually died out anyhow!

Mesh: yes, because of this. (points to PERFECT CHAOS picture)

Sonic: Chaos! (thinks to himself) exactly! Chaos eliminated the echidna race before, according to the visions Tikal showed me when we faced the threat of chaos. So what he says is true.. i wonder what knuckles would do if he heard abt this.

Mesh: But slightly before that actually, the sacred chao community already disappeared. without a trace, and without reason. and now all that's left of them is this temple.

(walks into third room. 1st room is chao garden. 2nd room is chaos picture)

Mesh: take a look at this. (points to broken tablet)

ok the tablet will talk abt the ultimate chao prophecy, but i'm too tired to think.

2005-04-06T08:17:00.000-07:00

"five went to outer space. one came back evil. four, came back FANTASTIC"

cracked me up big time. and my other frens too. but still going to watch it i think. wat i won't watch is "the invisible woman". why watch a show when u can't see the babe? i'm sure the human torch as a woman would be a hot babe though. (pardon my use of the word hot btw)

i kicked cerebus's ass in DMD mode for DMC 3. and no shit, the next mission, i fall immediately to those arrow shooting buggers. those arrows were a pain in the ass. and the arm. and the chest. they shot three arrows each time that's why. so wat did i do? i whacked them with the kalianna ann. no it's not a porn star. it's a rocket launcher.

did i mention i love my full stops?

2005-03-27T04:22:00.000-08:00

it can be said with much certainty that the lazy symbiote has taken over this body. yes all u friendly neighbourhood spiders and hardcore muggers beware. we're afraid of loud noises though. That, and pple who switch off the aircon when we're asleep.

DMC 3 was bloody cool. except each mission was so frustratingly long and my wrist hurt as if i jus did 50 push ups with my legs raised. bad enough i didn't even know whether it was painful or jus numb. but damn it was fun.

is eternity a line that stretches forever? or a dot? or does it have two sides?

2005-03-26T06:41:00.000-08:00

yishun safra's bowling alley's automatic doors scared me today. and i think i exclaimed so loudly pple cool hear it over the falling pins. yea BOWLING pins.

YES I SCARE EASY PPLE!!!

2005-03-24T08:19:00.000-08:00

slash, ramesh and i were sitting in the dispensary today waiting for ram's parents to pick us up. and we had like the most interesting conversation of the day. ram's story actually. now ram's actually, urm, horizontally challenged. challenged to stay within limits. if u get what i mean. so ram was telling us his story.

ram: so i was out with my two friends and we met this lady that i knew when i was younger. So i went up to her and said hi, and so she replied, "hello ramesh, i haven't seen u since u were small" (i hope i got the quote right, bro)

and one of ram's friends said,

one of ram's friends: wat ramesh u mean u were actually small?

so both me and slash were roaring with laughter, and ram reached out to get an oreo from the urm, oreo bag we were sharing from. and slash (real name shashi), made one of his best lines ever.

slash: u're still eating!?

well it seems some pple are having their b'days. last year's was my worst. but hey my dad's having his in two days. no idea wat to get. maybe a tie so that his dogs can play with something. ^_^ but yea everybody having birthdays today have fun!!

normally i get sleepy around this time, but it's like the natural valium in my system is suppressed by the speed at which my downloads are, urm, downloaded. the asylum that contains the loki though, has collapsed and the god of mischief is free. maybe not so much loki as opposed to urm, "the crank". yes in medical terms they call very very cranky pple, "the cranks". in my medical terms, that is.

ok half an hour after i wrote that, i think the valium jus won the battle of pearl harbour. no no. i think it jus demolished the great wall. -crumbles-

2005-03-22T04:34:00.000-08:00

so the mockery of six days of MC is getting to me. nope. not mine. damn i wanna extract my wisdom teeth too. where are they!?

pizza was tasty. i remember hating the sweet pineapples but now it seems they provide an antidote to the poison that is tomato sauce. seriously it's like ponstan to pain. and that jus makes me enjoy the cheese more. too bad my bro finished the pepperoni before i could start on it. got stuck on chicken wings.

today i realized that my appetite has decreased over time. so i had breakfast, brunch and after that i no longer had the urge for lunch! i mean, there must be some balloon in my tummy being constantly inflated whereas my tummy itself increases to a ln x graph. surely at some point they intersect and my stomach explodes. i still had lunch though. so it was noodles for breakfast, chicken rice for brunch and bah kut teh for lunch. i am greedy.

"we may not be great thinkers, or world leaders.. we dun read a lot, or run very fast, but damn it we can eat!"

2005-03-21T07:27:00.000-08:00

sigh. it's times like this, wasting the tranquil night away, accompanied only by coldplay, that spur me to write blogs like this. That, and diet coke with semicircular ice cubes.

now either my tummy's growling or snorring away. my mind is holding its own bloody sunday by shooting down all the other body parts that peacefully protest for rest. not going to waste a night like this away by sleeping.. hmm.. it doesn't really matter to me that i'm dead tired in camp. like school, camp is not. and if i didn't mind being tired in school, why should i in camp. so instead my fingers are forced to vomit out these words.

seriously i need to thank the coke.

so i was out with my senior today and she said something that made me feel so good:
"oasis is timeless."
ah made my day. Sorry i was a little off. strangely.

i'm actually thinking of my duck noodle breakfast tmrw. yes greedy like a man-eating raptor lusting for fresh human flesh. ok not so much that as opposed to vegetarians wanting spinach. no. argh i dunno anymore. it's the late hour! IT'S THE LATE HOUR!!

it's a champagne supernova in the sky. ah.

2005-03-21T05:47:00.000-08:00

i love my blog pink!

.. keep your thoughts to yourself.

so my math's in a bit of a low now.
my art though, high heh. if i do manage to get a scanner for below a hundred, a decent one at that, i'm actually considering uploading my comics online.
but it's rather irritating though, cos like chpt 1's super tiny, chpt 3's tiny.. only 4 and 5 are somewhat urm, readable.

and i will only upload once i refinish chpt 1 and 2. gosh. when, i have no idea. or maybe jus load chpt 3 up for fun. i love the fight between metal Sonic and Shadow.

anyhow, the course i attended had a lecturer with a really strong indian accent, thru no fault of his own though. but the program i need to learn is so frustrating that i'd rather eat spaghetti with a spoon anyday. So there i was, typing on wordpad at my com for fun and showing the lame stuff i was writing to my fren next to me. And then my fren asks for help, and the lecturer, she comes over and checks out my com. (we shared com) she saw the notepad file i typed and asked if she could close it. could i say no?

On it somewhere rather not discreet were the letters: "zzzzzzz..."

WHEN IS ADVENT CHILDREN COMING OUT?!?!?! everybody has to catch it. i heard "Ghost in a Shell 2" is coming out too for film fest in April. Ending film. WOW. the first one was slightly lewd but with enough effort it's possible to overlook and focus on.. urm.. other things.

ok now i need to add the links to my blog.. time to update the HTML.

2005-01-23T06:06:00.000-08:00

questions are here
http://www.unl.edu/amc/e-exams/e8-usamo/e8-1-usamoarchive/2004-ua/04usamo-test.html

strangely though i thought qn 2 was handleable. but on the mathlinks discussion site the half-solutions they put are so confusing.. but i think they got the idea. the crucial thing is if 2 of the a_i are coprime, then the 3rd condition is actually the division algorithm and it would lead to all the integers being in S.

for n larger that 2, we can always reduce the case to having jus three prime. There will exist 3 distinct primes in S at least, and we only need these 3 distinct primes to create the set of all integers.

Let these three primes be such that a less than b less than c. shucks i actually spent forty min thinking abt this when i started out blogging this entry, so this entry took a whole forty min.. cos i misinterpreted something. hai. thought i could think abt another problem.

this is so i remember also. for the sequence question in the Romanian TST, consider an equation (summation of i from 1 to n) of a_iF_i = 0 can be solved by F_n = (summation of i from 1 to n-1) b_i(r_i)^n, where r_i are the coefficients of the characteristic equation (sum i from 1 to n) a_ix^(i-1) = 0, and b_i are arbituary values solved by placing given parameters in. Cos to define such a sequence properly, we must have at least n-1 values of the sequence.

now i hope i didn't confuse any n's with n-1's here..

so i need to solve the quartic equation. how?
steps
1. eliminate the x^3 term by substituing a certain x value in. this leaves an equation x^4 + ax^2 + bx + c^2 = 0 (looks familiar) (i put c^2 for convenience)
2. then shift x^4 and c^2 over to the other side and complete the square with (x^2 + c + z)^2 for some arbituary z. that will be the LHS and so we have a quadratic in the right hand side in x.
3. we wanna choose z such that the RHS is a perfect square (has only one root in x), so we choose z such that the discriminant of the quadratic on the right hand side is zero.
4. the discriminant is always cubic, which has at least one real root. This will be z.
5. Square root and qed!

i think the problem here will be solving the cubic.. or maybe not. haven't worked out.

2005-01-23T03:14:00.000-08:00

HAHAHAHAHAH

and tmrw.. USAMO 2004.

2005-01-22T19:47:00.000-08:00

Damn. Had RT today and didn't know.. rushed to Khatib Camp in 5 min,.. Muahahaha

so i spent RT session thinking of my problems.. hmm..

Still dun understand question 1, so will sit on it for a while.

Question 2, the disc one has an errata.. for red colours, we will count 1 to n anticlockwise and for blue we will count clockwise.. solved this one. Arbituarily place the position of 2 n's and consider the sector between them. (not impt if the sector is actually zero) Now i can find a diameter that divides this disc such that the blue n is on one side, the red n on the other and also satisfy that there are the same number of blues on this side of the sector is the same as the number of reds as the other side. Then show that this diameter satisfies the conditions.

The geom question.. sigh.. still thinking.

The other two, super difficult strangely. The series one i think can use the finding roots of the quartic solution but that's too complicated and lacking elegance lo. The f(a,b) one, i checked the forum, and there's this short solution that doesn't make so much sense. The substitution solution makes sense though.. will brute force through.

2005-01-22T09:25:00.000-08:00

Ok problems to think abt for 23/01/05:
1. (S'pore mathematical medley prized problem) Let A be a set of n integers from the open interval (0, 2n). Is it always true that there exists elements in A whose sum is divisible by 2n?

2. (Romanian selection test 2004 Q5) Consider a disc divided into 2n equal sectors. Let the sectors be coloured either red or blue. Now we label the blue sectors and red sectors 1 to n per colour in a clockwise direction. Prove there exists a half disc that contains all the numbers from 1 to n.

3. (Romanian selection test 2004 Q6) Let a, b be positive integers, ab not equal to 1. Find all integer values that f(a,b) can take, where f(a,b) = (a^2+ab+b^2)/(ab-1).

4. (Romanian selection test 2004 Q7) Let a,b,c be 3 integers such that b odd, and let x_0=4, x_1=0, x_2=2c and x_3=3b, and for all positive integers n, we have
x_(n+3) = ax_(n-1)+bx_n+cx_(n+1)
Prove that for all integers m, and for all primes p, the number x_(p^m) is divisible by p.

5. (China MO 2004 Qn 2) A circle meets the three sides BC, CA, AB of a triangle ABC at points D1,D2;E1,E2;F1,F2 respectively. Furthermore, line segments D1E1 and D2F2 intersect at point L, line segments E1F1 and E2D2 intersect at point M, and F1D1 and F2E2 interesect at point N. Prove AL, BM and CN are concurrent.

Can look for the answers at www.mathlinks.ro and search for the solutions there..

jus to remind myself of the problems i wanna think abt

Cheers

2005-01-16T07:02:00.000-08:00

Chpt 2:
i haven't drawn this one cos i've been too lazy to draw Tails, so anyway

this chpt starts off with Tails in Grand Metropolis and he's "secretly" stealing info from Eggman's mainframe. Well secretly, because eggman actually knows he's there. Tails learns abit abt the evolution plan. He knows what Eggman wants to do, roughly, but decides to leave analyzing the results at home. As he sneaks off, Eggman sends a robot gift to meet him outside.

(I'm thinking big huge robot. Design not decided)

Then Knuckles comes in to save Tails. Basically it.

At the last part of the chpt, eggman will start to contact Mesh the Monkey and discuss with him the plan to trap Sonic as Sonic reaches the Forbidden Forest.

Note on Mesh: Monkey dude from the tribe of the F. Forest. He's the prince. He has a younger brother Meek who was saved by Sonic before. Explain more in Chpt 4.

Chpt 3:
Metal Sonic is given a second task by Eggman, to search for the ultimate creation gene, (i can't remember if it's for the gene or for the emerald Shadow's holding), and meets Shadow. Ok continue chpt 3 another day. enuff for today.

-gag-

2005-01-16T06:30:00.000-08:00

My story starts like this.. so far i've finished the first chapter (of which half of is in a plastic file i still can't find), i'm 3/4 way through the 3nd chapter, and 3 pages into the 4th. All this took me one year to do.

Which means i have to speed up.

Anyway.. back to the story.. hmm.. i'm sort of a diehard action/drama dude so my storyline may end up a little dragonballish.

and i talk too much.

Still the story.. it's abt Sonic the Hedgehog. It's been a dream for me to draw a comic of it, and whilst i record my musings, if it's worthy enough to be called that, won't really bother into explaining much of it or the finer details, so chill.

Story outline is basically abt the villain Mecha Sonic - not metal Sonic. It's the one that appeared only once so far in the entire Sonic Series.. it appeared at the end of Sonic and Knuckles, as Eggman's protector of the Master Emerald. So background has it that it was destroyed by Knuckles, after absorbing the Master Emerald's energy to become Super Mecha Sonic.

Here's where my story begins. Mecha Sonic, once he was abandoned by Eggman, did not shut down. Instead his Chaos Energy absorption ability sparked off a healing process, and in that process he became a powerful being, with a almost human mind and a robot body with the ability to freely synergize the Master Emerald's power. I haven't decided exactly what Mecha Sonic wants to obtain or do though..

So Chapter 1:
Sonic basically discovers that the Chao creatures are going missing across Mobius. Sonic thus goes to the Angel Isle's Chao garden to confirm his suspicious. Upon reaching, he meets Espio the Chameleon and a final last Knuckles Chao. Metal Knuckles then appears luring Sonic away into battle. Metal Sonic then turns up and captures Espio and the last Chao. Little is revealed abt Eggman's plot to produce a final and most powerful evolution of Chao, more powerful than the Chao Guardian, Chaos, himself. And M.Knuckles and Sonic will battle off with M.Knuckles losing.

"When the Master combines with the Being, the new world will begin"

By Master i mean the master emerald user, Mecha Sonic, and the Being would be the final Chao evolution, name of which i have not thought off.

let's talk abt this final Chao thingum first. Eggman has retrieved stones from the Forbidden Temple, where Sonic will visit in Chpt 4, which have ancient writings of the future of Chao. The evolutions of Chao will reach a stage where it will finally reach a suitable final state to fulfill the true duties of Chao, to protect and harness the Master Emerald, for good of course. But Eggman wants this another way round.

Eggman, is trying to speed up the evolution process by genetic engineering, extracting genes from all Chao, and using Espio's chameleon gene shifting ability to speed the process up even more.

He needs a Topaz Crystal to fully initiate the adult evolution, which he tricks Tails into getting for him (this is a later chpt which i haven't decided).

This being will eventually merge with Mecha Sonic for the final battle. Leave that for later.

2005-01-16T06:23:00.000-08:00

Kinda re-kickstarted my blog.. think it's been too long a while that i've been sitting in front of the com and having nothing to do.. those times when i dun feel like thinking or drawing and when i dun really have anyone to hang out with.

I dun really like to say personal stuff anymore.. might lead someone to misunderstand..

anyway the main purpose of this blog is not for personal stuff.. it's for my musings.

And yes the stuff posted here may seem irrelevant, childish.. blah.. might touch on God but we'll see how that goes. I dun really think I've much zhi ge to talk abt Him anyway.

more like.. since i'm like drawing my comic, i've no where to like write down my ideas or anything like that.

So this'll be the place it'll be lo.

and with that it begins.