## K’s Semi-solution to “Hard Problem”

September 19th, 2009

I can’t think well after lunch, so I don’t have the solution. But I know you have to have the travelling times of each individual equal each other. And they have to share the bike. x=distance girl rides on bike, y=distance of boy on bike, z=distance of dog on bike.

$x+y+z = 38$ $16(38-x) + 6x = 15(38-y) + 5y = 10 (38-x) +4z$

I think I’m on the right track ,but if not, well, there’s a reason I’m not trying out for math team. Ok, people are coming over to work on the English project now.

Edit/Ben: You’re thinking on the right track with systems of linear equations, with three variables. However, I don’t see why you set $x+y+z = 38$, because $x+y+z$ is the sum of the time the girl, boy, and dog ride the bike, and that shouldn’t have anything to do with the distance they travel. As for the second equation, why are the three equal?

Continue >.< or leave it to Hanchan when you guys finish with your projects.

Edit/2: On second thought I shouldn’t really barge into your post, I should write a comment ^_^

## Hard Problem

September 19th, 2009

A boy, a girl and a dog go for a 38 mile journey. The girl takes 16 minutes to walk a mile. The boy takes 15 minutes to walk a mile and the dog can trot a mile in 10 minutes. They also have a bicycle which only one of them (including the dog!) can use at a time. When riding, the girl can travel a mile in 6 minutes, the boy can travel a mile in 5 minutes and the dog can pedal a mile in 4 minutes (what a marvelous dog!). What is the shortest time in which all three can complete the trip?

Credit for problem goes to Dr. Kevin Wang (not sure if it’s by him or not).

Good luck. Post solutions as blog post or comment.

## The Racist Coin Problem

September 19th, 2009

Hank has 744 black coins and 527 white coins. He wants to arrange them in stacks of the same kind of coins (since if differently-colored coins are placed together in the same stack, discrimination will eventually result in hate crimes and lynchings). In other words, all coins in a stack are all black or all white. If each stack has the same number of coins, what is the minimum number of stacks needed?

## AT&T needs to go to hell.

September 19th, 2009

As you can tell, I’m mad.

Suddenly, at like 12pm today, my internet completely died?

Why? Because AT&T decided to upload a firmware upgrade to my router. WITHOUT MY CONSENT.

Needless to say, that is troublesome.

More frustrating was that the firmware upgrade f***ed up my entire network configuration. It started telling me that “ooh ooh! You have a second router behind me! I DON’T LIKE THAT! *blocks internet*”

Ugh! I like my WRT54G with DD-WRT custom firmware installed! It’s the awesomest router ever! I don’t want this piece of c*** 2wire router that AT&T almost wanted to charge me for!

And now they’re complaining about my second router and not letting me use the internet… guess what?

THEY ERASED ALL MY SETTINGS!

I have a complicated set up that allows me to host a webserver behind two NAT routers (lol, extra extra firewall XD)… and does AT&T Yahoo care? No, of course not.

So, long story short, got everything working again after hours of messing with stuff (and not having internet… meaning webserver down). Thank goodness for DD-WRT. I can get a tunnel set up for my HTTP server within 2 seconds. Click, click, done.

Guess what? I can’t even set up ANY type of redirection/tunnelling on the 2wire router anymore. WHY? BECAUSE THE INTERFACE IS NOW COMPLETELY BROKEN. Well, not that it wasn’t broken before, but now it’s completely unusable. AT&T must have f***ed something up while adding their logo to every single page, and broke every useful function on the router.

Okay, I’m tired, and tomorrow I need to wash cars that I paid for myself. Basically, we pay the Music Club for getting our cars washed, and then we go out and wash our cars ourselves.

## Perception of Japan: Stolen from cracked.com

September 18th, 2009

For you Japan/anime obsessed guys

Perception of Japan: 1900

## Number Theory – Solutions

September 18th, 2009

1) Written out in base 10, the number $345!$ ends in how many zeroes?

Each zero in a number represents a factor of 10, or a factor each of five and two.

Therefore, to find the number of zeros after a number, we need to find the number of factors of five and the number of factors of two in $345!$.

How many factors of five are in $345!$?

Simply divide 345 by five.

$\dfrac{345}{5} = 69$

However, we need to count the factors of five squared (25) twice, so we divide again by 25.

$\dfrac{345}{25} = 13$

And finally, let’s not forget the factors of five cubed which need to be counted three times.

$\dfrac{345}{125} = 2$

Summing these together:

$69 + 13 + 2 = \boxed{84}$

Thus there are 84 zeroes after the number $345!$.

2) The product of the 12-digit number $493,\!224,\!762,\!945$ and the 12-digit number $471,\!910,\!894,\!925$ is the 24-digit number $232,\!758,\!139,\!280,\!5A5,\!928,\!554,\!125$. Find the digit $A$.

Did you try to find the digits that affected the value of A and try multiplying things out?

A smarter solution, do this calculation mod 9. It’s called “casting out nines”. Cross out all the nines and all the numbers that add up to nine, etc, and add up the remaining numbers, subtracting nine when needed.

$493,\!224,\!762,\!945 \equiv 3 \mod 9$ $471,\!910,\!894,\!925 \equiv 5 \mod 9$

Therefore,

$493,\!224,\!762,\!945 \cdot 471,\!910,\!894,\!925 \equiv 15 \mod 9$

And

$15 \equiv 6 \mod 9$

The product mod 9 is:

$232,\!758,\!139,\!280,\!5A5,\!928,\!554,\!125 \equiv 2 + A \mod 9$

And since the products are supposed to be equal, they will also be equal mod 9.

$2 + A \equiv 6 \mod 9$ $\boxed{A \equiv 4 \mod 9}$

It’s as simple as that!

## Too much anime here, here’s some sports to neutralize it

September 18th, 2009

Current statuses of my sports teams:

First:

Offseason right now, not much going on. We have signed Ron Artest

## Number Theory

September 18th, 2009

Exercises for Hanchan:
(note to self, move this to private/password protected tomorrow)

1) Written out in base 10, the number $345!$ ends in how many zeroes?

2) The product of the 12-digit number $493,\!224,\!762,\!945$ and the 12-digit number $471,\!910,\!894,\!925$ is the 24-digit number $232,\!758,\!139,\!280,\!5A5,\!928,\!554,\!125$. Find the digit $A$.

Hey, Ben, this is K. Apparently I can edit this. I can also see all your private posts. You should probably fix this.

Fixed. Thanks.

## In our local hospital, they sell tampons in the mens’ restroom

September 18th, 2009

It’s true. I went in to a restroom in Methodist Hospital (where I volunteer every other week)… and… there was a tampon vending machine…

… ahem. Anyways, I watched Hayate2 ep #24 today (2nd to last episode), you can find a colorful picture review in the updated post a couple pages back.

Also, like half of this website/blog is tagged as private (only I can see my private posts), because I originally created this to be more of like a diary, but you guys are nosy and want to know all about my life so ~_~

Well, last hayate2 episode should have aired by now, and other final episodes are all coming out. Fall will officially start like next Tuesday, and along with that, will come the Fall 2009 anime season. ワクワク～～

oh, and HOORAY my cold is (mostly) gone. I love not being sick. It feels so normal. Ugh. When I grow up, I’m seriously going to engage in battle with the cold virus and eradicate it from the face of the planet. Pfft, stupid rhinovirus.

I feel like posting a math problem. Hold on, lemme think of one.

## America’s coin system is fundamentally racist

September 17th, 2009

We had an interesting conversation in English class today. Our teacher, Mr. Villalobos, told us to come up with as many archetypes as we could for a penny he gave us. (We were studying archetypes… so…)

Well, the discussion went like:

“Oh oh Abraham Lincoln! the penny can symbolize peace!!”

“Yeah! And non-racism!”

“But… the penny is dark-skinned, you know? It’s a black coin!”

“And the penny is worth the LEAST out of all American coins! The White coin, the quarter, is worth twenty-five times as much as a Black coin!”

“It’s the most worthless coin out of them all! Nobody wants a Black coin, people just toss them onto the sidewalk and let them get run over by cars…”

“… guys… stop being racist…”

“Oh, if you think that’s racist, what about dollar coins? They’re Yellow, or um Asian, and they’re worth a hundred times as much as a Black coin!”

“…”

“…”