Penny Problem!

Math

I subbed in for the Calc teacher again. One student showed me a neat puzzle involving pennies! Seriously, try this out using actual pennies/etc.

I totally recommend finding four pennies and trying this out before looking at the solution.

If you can't see the animation above, here's an explanation:

Objective:

Move the pennies into a straight line, any direction.

Rules:

• Move only one penny at a time;
  
• Pennies may only be moved to a spot where it will touch at least two other pennies;
  
• Pennies may not be picked up (you may only slide them around);
  
• Use as many moves as possible, then try to minimize the number of moves.
  

To start, four pennies are arranged so that each penny touches two others; a parallelogram.

If you found that easy, try the next step--use five pennies:



Seeing the Solution

I think the difficulty comes in seeing the line we're trying to build. We're so accustomed to perpendicular lines that we can't see the 60-degree lines until we've physically moved the pennies around for a few minutes to get used to it.


The Solution

Really, the trick to creating a line in the least amount of moves is to make a gap large enough for a single penny. The last move will be to fill in the gap--no other move can be the last move.

At least four pennies must be present for this; but because of the initial arrangement (a "diamond" shape), this is not necessarily intuitive. To build the gap, you must first build a column of three. Then, you must be able to see the line.

With five set up in one column of three and one column of two, the process becomes more obvious--simply remove the middle penny in the column of three.

From there on, it's the same game: make a gap, and stagger the pennies to build the rest of the line. It's interesting to note, though, that the minimum number of moves is equal to the number of pennies! I found that pretty exciting!

I'll figure out a proof for it, some day... I've still got another proof to figure out; it's for a card trick, and I get the feeling it uses Perms and Combs, which sucks for me.

--Charlie!

PS: Happy Mothers' Day!

"Protection"!

Kay, so one of my buds started talking about 300 again.

E--- (1:01 AM):

it's a guy movie
yay!

Me (1:01 AM):

haha, aye

E--- (1:01 AM):

We all want to be warriors
in some way :P

Me (1:01 AM):

Really? Explain!

E--- (1:02 AM):

lol
are you serious

Me (1:02 AM):

Well, in what way do guys want to be "warriors"?

E--- (1:03 AM):

we have a natural drive to become physically fit and protect our women :P
thats as basic as I can make it

Me (1:03 AM):

;P Are you saying I'm incapable of understanding something that isn't basic?

E--- (1:03 AM):

no
im saying im lazy

Me (1:03 AM):

:P Just foolin'
Why do guys want to "protect" women?
From what do we need protection?

E--- (1:04 AM):

in this day, nothing
we feel that protecting you is a way of showing we love :P

E--- (1:05 AM):

it's a natural thing, or even just doing silly stuff like opening the pickle jar haha

Me (1:05 AM):

Hmmm, okay

E--- (1:06 AM):

im not in a relationship right now so I don't really want to protect anyone
from the invisible monsters
I don't know how to explain it :\
a natural urge to take charge ?
I don't know about women but men like to work out because they get a feeling of invincibility
as well as extreme satisfaction
:P

I wonder, what do women "need" to be protected from?

Seriously, the first thing that came to my market-researcher-mind was "Protect against leaks and odours!"

I want to make a movie called "The Cycle of Bloodshed" and have it totally be about menstruation. Seriously. Here's a teaser:


You can also view it here.

[post abandoned]

--Charissa

Art and Stuff

I realized, the other day, that I'm not making as much art as I would like. And since Autumn passed me by uncaptured (by camera and canvass), I decided the next piece I do will be "epic" and about Autumn! Here's a "sketch" I've made of it in Flash MX.

(I still can't believe Adobe bought Flash... The version I use still says "Macromedia Flash MX" on it.)


New Loading Screen on Intro to Epsilons and Deltas

Also shown here.

Epsilons and Deltas is a little animation that I've been working on for about a year. It's a short story about Math and Love. Awwww. It also features two girls, a strip from xkcd, and La Campanella by Franz Liszt.

The old loading screen didn't have red-bowtie-girl running along the loading bar; she just stationary-ran beside the percent-loaded display, and it looked a little tacky. This one has a nicer "floaty" and "Ooh, numbers!" feel to it, which I don't mind at all! But, we'll see if I can even still improve it...


Other Stuff

My eldest brother went back to school in January, and has asked me to help him out with derivatives! I think I'll do another of those Flash tutorials like in the previous post.

He's also sending over a box of goodies from Germany! There'll be Lebkuchen, my favourite kind, with the candied orange peel inside and wafer on the bottom and either dusted lightly with powdered sugar or coated in chocolate! Mmmm! Also, a digital camera and computer gear!


Events

Nov 01

I'm Employee of the Month! Hoorays, I guess!

Nov 05 (today!)

Grocery shopping. Hells yeah.

Work at the Reserves tonight. Hells yeah...

Should call the bakery to pre-order special bagels.

Should drop by the library to return Dragons in the Water by Madeline l'Engle; and take out another Origami book and Math book.

Nov 06

Meet up with the teacher to lend him the entire S4 Pre-Calculus curriculum... I'm wary of lending that to anyone, and of all people, him...

Should swing by the bakery for more bagels... Mmm, pumpernickel bagels...

Also hoping to spend some good time with my best friend Eric!

Should also swing by the Rainbow Pride group at the university. I haven't been there in ages--mostly because I'm trying to avoid someone.

Nov 09

Kevin's birthday party, at last!

Nov 10

Homo Hop, a queer-oriented social. I'm not sure if I'll go... We'll see.

That's all for now. I should get some work done today.
--Charissa

018: Exponentiate!

Woo! Just a quick update to post this tutorial (Flash) on exponents/radicals. Check it out here, too!

Woots. Off to work now.
--Charissa