ch3cooh: (Ball Pit)
Challenge: write up your initial instinct, then try to prove it and let me know what happens. :D
I really like this puzzle.  And I'm sure that there's a simpler proof than the one I'm using right now.

Puzzle:
GeometryArea

Solution )
ch3cooh: (Ball Pit)
Being in the right place and having enough time to draw a real picture is hard.  But a few months ago, I found myself really wanting to draw more, and eventually I also found a good compromise: a phone app called "Draw Something." It's effectively digital pictionary, or at least that's the intent.  The best part of the app is that, when you receive a picture, it plays out a 3x speed video of the picture being drawn, instead of just showing you the final image. I like both the drawing and the watching other people draw - trying to guess their word as quickly as possible.  You also get to see your partner watch your drawing and guess your word - an again sped up movie of them putting the letters in place when they realize what the picture is (or sometimes trying and getting it wrong a few times first.)

On top of that, I've been abusing the program in a way - using it to draw entire scenes in addition to communicating the word. :) There's a limit to how much "ink" you can use (which prevents me from spending forever on a single picture).  And there's also an immediate objective and audience every time I draw.  It's been a pretty perfect solution.

Here are some examples, and more of my pictures are hidden below.  And if you think this sounds interesting and want to try it, maybe invite me to play a game with you (my username is "ch12cooh"), or I can invite you if you let me know you're intersted.

app link

Sushi, Mars, Sphinx, Hayride, Ocean...

IMG_20141014_025032IMG_20141012_054738IMG_20141012_063244IMG_20141026_001454IMG_20140521_202826

More pictures! )
And here are a few pictures that other people on Draw Something drew for me:

2014-10-14-00-09-022014-10-18-15-36-432014-10-20-00-20-442014-10-22-01-01-162014-10-24-19-18-52
ch3cooh: (Fringes of Chaos)
These pictures are from the Elementary math circle program at SFSU.  It's a class I teach every Thursday with a coteacher, Josh R. :)  I have never taught with a coteacher this extensively before -- it's awesome!  One of the best parts is that he and I have very different mathematical backgrounds, so whereas the Graph Theory class I'm prepping for next week is foreign content for him, the past 3 weeks that we've spent studying sequences, building up the the Collatz conjecture is new content for me.

The ribbons the students (and instructors) are playing in are sequcens that start with any number of the students' choosing and then progress using the following rules:  If the latest number is even, divide it by 2 to find the next number.  If the latest number is odd, multiply it by three and then add one to find the next number.  The magic is that, so far, every initial choice of a number eventually leads to the same behavior - eventually, the sequence trickles down to the cycle 4-2-1.  But it's unproven if this is true for ALL numbers... it just works for all of the billions tested so far. :D  And sometimes it takes a while for the sequence to get down to that cycle.  For example, our TA chose to start with the number 231 which has a sequence that goes for 127 steps before cycling.


I want to try a similar session out with an older group and combine it with logic tables of pairity. :)  And I think this might be the last part of an "infinity" curriculum that I've been trying to piece together! :D

20141016_180015 20141016_181753 20141016_181547
ch3cooh: (Winter)
Both of these series are amazing.  Mistborn is 3 books long, but part of an enormous unfinished universe.  The three books stand alone though and, if you like epic fantasy at all, or plots that are masterful puzzles in any genera, read these.  Rated on 3 axies: World Building, 9/10, Plot 15/10, Characters 6/10.  The Wheel of Time seems similarly epic, slower, but more intriquete and the characters are a lot stronger in my opinion: World Building 9/10 (but very different), Plot 8/10, Characters 9/10.  The series is 14 books long however, which is... intimidating.

And there aren't any spoilers in the details below, just big-picture writing/style observations. :)

:) I finished the Mistborn series a while ago, but then had a rough and busy couple weeks.  However, wrt the end of Mistborn: IT. WAS. PERFECT!  Really in pretty much all ways I can measure, it was such a satisfying conclusion. The plot and world-building are impossibly well crafted and last quarter of the 3rd book is one ridiculous climax atop the next, paying off absolutely everything. After reading the first book, I thought, "OK, that was good...' but I probably wouldn't have continued the series if not for a very strong recommendation.  Now I pass that recommendation on with equal intensity. :)  And I'm reading the Wheel of Time series now, in part on the premise that if Brandon Sanderson pulled the ending together, it won't disappoint.

However, it's really the differences between the series that interst me/prompted me to write this entry.
More in-depth comparison, still no spoilers though. :- )

ch3cooh: (Cell Phones)
Woot! I survived the week!
MoMath has been very very full of school groups for the past few weeks.  I've been teaching 5 or 6 classes nearly back-to-back every day.  Mainly Cryptography though, which is my favorite of our three classes.
But I'm finally settling into the 'routine' of this, and re-finding the time and energy to do other awesome projects at home on the weekends. :)

Way back in January, a bunch of friends sent me amazing pictures... and I got hosed and hoarded them all to myself.  No more of this.  Here are the results (my favorite pictures) from week 2 (of 4)  More soon.

Category 1:  ID -- Can you ID the subject matter of each of these shots?  (hints behind the cut)
Capture(Hidden)
hints/full images )

Category 2: Sometimes the subject matter is simply awesome
Capture(Things)
full images )

Category 3: Beautiful Locations
Capture(Places)
full images )
ch3cooh: (light on black water)
I'm about to teach a summer math course: Proofs and Visualizations (it's gonna be awesome!) and I've been talking about the problems/units with a bunch of friends.  One of the units is based on a math puzzle called "The Paradox of Perfectly Logical Pirates"  I've outlined the problem below.  However, here's the glitch - once you've come up with the straight-forward answer, here's another question:  Two twin brothers, Alfie and Ben are given $10 of allowance every week.  More specifically, Alfie's given the money and his father tells him to split it between himself and his brother Ben.  As long as Ben accepts the split, the boys get to keep the allowance, but if Ben ever complains, neither boy will get anything.  Alfie and Ben are logical kids, and both realize that something is better than nothing.  So, each week, Alfie gives Ben $1 and keeps $9 for himself.  And Ben doesn't complain because $1 is better than nothing.  But then, one day, Ben goes over to his friend David's house.  David's twin sister, Kate, has just been given $10 allowance to split between herself and David - their father has the exact same rules.  Perhaps David is more sure of himself or something, because he's decided that he'll reject the split unless his sister Kate gives him $5.  Since Kate wants to keep getting allowance ($5 is better than nothing) - she splits the money evenly between them each week.  Ben sees this and is surprised and impressed.  Can he get the same results from his brother Alfie?  Later that week, Ben visits his friend Fanny's house, although Ben doesn't like Fanny all that much - she's  a bit greedy and reminds Ben of his brother Alfie.  When Fanny's brother Elmo gets $10 of allowance to split between the two of them, Fanny tells Elmo that she'll complain to father unless Elmo gives her $9.  Elmo believes her (she is a greedy one) and would rather get $1 than nothing, so each week he gives Fanny $9.  Sometimes Ben wonders if he could get Alfie to do this for a while at least - just in order to pay him back for the many weeks of taking $9 for himself. 

In real life, who has the power? - the person splitting the money, or the most stubborn and greedy player? Why?  How can this question be described rigorously mathematically? 

The Paradox
of Perfectly Logical Pirates )

I'm really thrown by these puzzles/'paradoxes' and I feel like there's got to be a good theory somewhere to explain what's going on.  I also think these questions are practically relevant since they suggest that things like mutinies might have a logical basis, whereas simple economic theory frequently predicts that the masses will just accept their short-changed fate. 
ch3cooh: (Insomnia)
Answers to this question either of the practical nature, or of a mathematically interesting nature would be much appreciated!

THE PROBLEM
I'm currently scheduling interviews for teaching positions in a summer camp (Junction, an MIT ESP program) I talked with the interviewers and made a schedule of all of the interview slots during which we can convene for interviews. Now I need to email a bunch of prospective teachers and somehow learn enough of their availability to schedule them each for an interview. I'd like to do this without too much email correspondence back and forth since it's a lot of people to keep track of. My current plan is a bit complicated and something less complicated or technology that would help with this would be very appreciated.

THE PROBLEM MORE RIGOROUSLY
There are 35 good interview slots and another 16 ok slots. But for convenience, I'll simply say there are 51 slots. I'll call this set S (interview slots). S is a finite set of non-overlapping hour long intervals between February 21st and March 5th. They are either from an hour to an hour (ex:5pm-6pm) or from a half hour to a half hour (ex:5:30pm-6:30pm). They are distributed irregularly within the range of Feb 21st and March 5th. 20 teachers currently need to be scheduled for interviews, I will call the set of teachers, T. And each Teacher, t_i, has a subset of the interview times that they would be able to make, A_i < S. What is an efficient way to get information from each teacher about their A_i in order to find a unique interview time for each teacher? To further specify 'efficient', let's say that I don't want to ask for more than 10 bits of information in an email, and I want each teacher to need to send me as few emails as possible.

An algorithm that is communication efficient but not always the best is ok (EX: normally requires 2 passed emails with a handful of exception cases where 5 emails may be necessary). However, in this case, know that the trend in my past experience are that some people are very busy and some people are very flexible.

CURRENT PLAN
Right now, I'm planning on emailing them all a google form that asks for a bunch of basic info about their class. And, at the end of the form I would ask them to select a subset from a list like this:
Morning of Sunday Feb 21st
Late Evening of Sunday Feb 21st
Early Evening of Thursday Feb 25th
Late Evening of Friday Feb 26th
Where they select an entree if they are available for most of that time range.
I define each time-range of day as follows: Morning (9am-12:30pm), Afternoon(12pm-3:30pm), EarlyEvening(3pm-6:30pm), Late Evening(6:30pm-10pm)
I would then email each person two or three time slots to choose between within one or two of their specified time zones. And they email me back a final time selection.
So:
1) They get an email from me
2) They fill out a form
3) I send them a couple times to choose from
4) They pick a final time

But, honestly, this feels way too complicated! So a better method (from either mathematical or practical experience) would be awesome!

THANKS!

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