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[Andir]

At my place of work we have walls that can be written on with dry erase marker.

I got to thinking just tonight on what would be a geeky/neat way to keep up on (or refresh Math in my case) problem solving skills and get some socializing/competition with my co-workers.  (It's a room of programmers...)  I decided to see if I could find a site dedicated to daily/weekly posts on Calculus/Geometry/Algorithm related problems that I can post on the board.  I'd write up some on my own, but I also want to solve the problems instead of having to come up with new problems every day.

I was wondering if anyone knew of a site off hand or even a book full of progressively trickier questions that I can post and see who emails me the correct answer first.  Just for friendly competition. I eventually want to throw in some challenges like "Write a single method to solve for the Nth Fibonacci number" to see how people respond, but I wanted to start off light and fun.  Some simple "solve the area of this shape" evolving to "solve for x" Calculus.

Any comments, tips, websites?  (My Google Fu has found a few sites that cover daily questions.  Some are higher level than I'd like to start with... some aren't very organized.  I'll probably start with something like this [even though that's a bit higher than I'd like to start, maybe just cover shape area first...  I don't want to scare anyone off of joining in] and just wing it if I have to.)

[Eidolon]

If you haven't already heard of it, Project Euler is a good brain-challenge. Doing the problems without any computer programming knowledge might be difficult though (to be honest, I've only gotten through the first couple, so I'm not sure how much harder it gets ).

I heard a set-theory related brain teaser a while back, let's see if I can recall it correctly:

Spoiler (click to show/hide)

You have a set of numbered balls, starting at 1, 2, 3, going to infinity (so, countably infinite  ). You also have an infinite-size bucket to put them in.

   It is currently 11:30pm. Halfway to midnight (11:45), you will put balls 1-10 in the bucket, then remove number 10 from the bucket.
   Halfway again (11:52 and 30 sec) you will put balls 11-20 in the bucket, then remove number 20. You'll keep doing this each half-amount to midnight, putting in 21-30, removing 30, 31-40, removing 40, etc. When you reach midnight, you will have balls 1-9, 11-19, 21-29, all the way to infinity left in the bucket. There will be an infinite amount of balls in the bucket, and you will be able to describe which ones are in (all that aren't a multiple of 10, for example).

  Now, you'll do this again. This time, you'll put in 1-10, then remove number 1. Then you'll put in 11-20, and remove number 2. Then 21-30, remove number 3, and so on. By midnight, which balls will be in the bucket, and why?

I feel like I've over-explained it a bit, but the answer is:

Spoiler (click to show/hide)

 There will be no balls left in the bucket. For any ball put in the bucket, you can calculate what time it was taken out. Despite the fact that only one ball is taken out each time in each case, the way you counted them matters. This is something of a counter-intuitive truth.

IIRC, a person from the Game Maker forums I used to frequent, named Yourself, posted that on a blog, so you might be able to dig that up if you wanted a better description.

I imagine that a more-educated math person is going to find a way to tear that down, but whatever. 

[Narushima]

http://www.rankk.org/

You could also simply doodle a penis, like everyone else. No need for fancy stuff.

[Andir]

Both Excellent resources, thanks!  We already have miscellaneous drawings all over the place.  I wanted to get people more involved though.  I was trying to think of a way to let the "winner" put up a new problem for people to solve, but that may get into a pissing match on who comes up with the most esoteric problems and I want to keep it open to everyone.

I actually already had Project Euler on bookmark for some of these.

[Brackev]

I feel like I've over-explained it a bit, but the answer is:

Spoiler (click to show/hide)

 There will be no balls left in the bucket. For any ball put in the bucket, you can calculate what time it was taken out. Despite the fact that only one ball is taken out each time in each case, the way you counted them matters. This is something of a counter-intuitive truth.

Ummmm...

Spoiler (click to show/hide)

According to my math skills, infinite total balls is 9x bigger than the infinite that was taken out.  Therefore, there balls in the hat are (inf/9) to (inf).  This is an irrational problem so an irrational answer is required.

[Funk]

 well it is a new day here, so can you some one check my maths

Code: [Select]

π x79.5mm x 73.4mm x 4 / 4
= 1716
             

[Vector]

Ummmm...

Spoiler (click to show/hide)

According to my math skills, infinite total balls is 9x bigger than the infinite that was taken out.  Therefore, there balls in the hat are (inf/9) to (inf).  This is an irrational problem so an irrational answer is required.

You're wrong.  I'm not going to say any more, because that would spoil it for you when you get it.


More on-topic, I might actually have something, but if I put it here it's going to be a while.  Good luck with this--it sounds really cool.

[Andir]

well it is a new day here, so can you some one check my maths

Code: [Select]

π x79.5mm x 73.4mm x 4 / 4
= 1716
             

It should be ~ 18332.135611492520484401062934451mm^2  I'm not sure how you got 1716.

In Math and Computer Science, the multiply/divide are equivalent so you process from left to right:
PI * 79.5 = 249.75661596038856245778014897072
249.75661596038856245778014897072 * 73.4 = 18332.135611492520484401062934451
18332.135611492520484401062934451 * 4 = pointless because you're going to divide it by 4 next.


WolframAlpha

More on-topic, I might actually have something, but if I put it here it's going to be a while.  Good luck with this--it sounds really cool.

Thanks.  I was kind of wondering if you'd show up.  I didn't want to pollute the other topic you have going with the question.