So here's the solution which seriously took me all day to come up with. Because I'm pathetic. (I kept forgetting about the clock strikes, which really is the key here.)
So... after she makes the statement "I see at least one red hat", the clock strikes 14 times without anyone doing anything, and then on the 15th time, all 15 people with red hats get up and leave.
This is why:
If there was only one person with a red hat, he would know it was him immediately after she made the statement because he would look around and see all blue hats. So as soon as the clock stuck, he would leave. BUT, if there were 2 people with red hats, they would each look around and see one person with a red hat, and thus would be able to make no conclusion about the color of their own. Then, however, the clock would strike once and no one would leave because the 2 people with red hats were not able to conclude they had red hats on. However, as soon as this happened they would realize "well that guy with a red hat must be seeing another red hat, because otherwise he would have left, and since I can only see a bunch of blue hats, and him, I must have a red hat as well," so the second time the clock struck, they would both leave. If there were 3 people with red hats, they would each look around and see two others, and following the same reasoning, they would assume both of these people would leave on the second strike. When they didn't, each would conclude "well, those two others must EACH be seeing two red hats, and since I only see two, I must be the other one" so on the third clock strike they would all 3 leave. So it just continues all the way up to 15.
Cool, huh. Of course, in real life they would sit around talking about Michael Jackson and completely forget about the hats...
Anyway, it's just interesting because the guest didn't tell anyone anything they didn't already know, and yet as soon as she made her statement she set off a chain reaction (assuming these are all logic-minded individuals or math nerds or whatnot) so that they would all leave after the 15th clock strike.
That's all.
S
Monday, June 29, 2009
Friday, June 26, 2009
Mathematical Induction
A group of men, all versed in logic, sits around a table. Fifteen of them are wearing red hats, the rest blue. Each can see the others' hats but not his own. On the table is a clock which strikes once each hour. The men are given the following instructions: 'You are not allowed to discuss the color of your hats. However, should any of you find that he is wearing a red hat, he should leave the table on the clock-strike immediately following his discovery.' Now it is assumed that no one is initially aware of the color of his own hat. Furthermore, since the men cannot see the color of their own hats, nor discuss it with their colleagues, nothing happens for a while. Then a guest arrives. She looks at the hats around the table, and says, clearly: 'At least one man here is wearing a red hat!' What happened and why?
"An induction argument can be used to show that once the guest has made her announcement all individuals with red hats will eventually leave the table. This contradicts one's feeling that nothing should continue to happen; after all, apparently the guest has not provided any new information."
After I thought and thought about this for way too long, the answer just popped into my head and it was so freaking simple I was annoyed at myself. Induction is kind of cool.
"An induction argument can be used to show that once the guest has made her announcement all individuals with red hats will eventually leave the table. This contradicts one's feeling that nothing should continue to happen; after all, apparently the guest has not provided any new information."
--Mathematical Fallacies, Flaws, and Flimflam
After I thought and thought about this for way too long, the answer just popped into my head and it was so freaking simple I was annoyed at myself. Induction is kind of cool.
Wednesday, June 10, 2009
A rose by any other name (x 200)
I just cut the stems on 200 roses and put them in water. Pictures to follow.
The gift of Magic
I gave a friend magic for his birthday. I don't know if he appreciated it. I'll elaborate on this later.
Sunday, June 7, 2009
The christening of Serenity
My little brother Nathan built a kayak and I was lucky enough to be here for the christening and maiden voyage this morning.
Getting it off the car.
He decided to name the kayak Serenity. My brother is a geek. Wonder where he gets it from.
In the water for the first time.
Christening it with ginger ale (because we had no champagne bottles to break over the side) and saying the christening prayer that Nathan found online: "Please float please float please float please float..."
The maiden voyage.
It floats!!!
After Nathan established that it wasn't going to sink, the rest of us took rides. I was impressed at how well it handled.
Getting it off the car.
He decided to name the kayak Serenity. My brother is a geek. Wonder where he gets it from.
In the water for the first time.
Christening it with ginger ale (because we had no champagne bottles to break over the side) and saying the christening prayer that Nathan found online: "Please float please float please float please float..."
The maiden voyage.
It floats!!!
After Nathan established that it wasn't going to sink, the rest of us took rides. I was impressed at how well it handled.
Saturday, June 6, 2009
A nice day in Boston
Monday was a really beautiful day in Boston. I really wanted to be outside enjoying it rather than in the office. Being the annoying person that I am, I pelted Nate with "let's go to the park" on gtalk until he finally gave in. Actually we were debating going to Star Trek, so we met at the Common, but then I made the executive decision that we should walk around the Public Gardens and the Common instead, so we did. The weather was nice; I had a great time, and we were able to have a lot more interesting conversation than watching Star Trek would have afforded. (not that I don't love Star Trek... I still totally want to see it again.)
We saw the Make Way for Ducklings statue, and some nesting swans, among other things. I have a couple pictures.
It was fun. :)
We saw the Make Way for Ducklings statue, and some nesting swans, among other things. I have a couple pictures.
It was fun. :)
Tuesday, June 2, 2009
What the world wants to make, v. 2
Google search suggestions for "how to make..."
***NEW*** I'm feeling lucky search results included, with commentary...
how to make a website
The result of this search brings up a hideous yellow and blue website entitled "How to Create a Webpage" that SHOULD be called "the perfect example of how NOT to make a webpage," or maybe "If you want absolutely NO ONE to take you seriously, take your webpage-making advice from us!" After close examination, I realized this site is a fossil of the internet days gone by. The first piece of advice for making a website is "There are basically two ways to make a web page. The first way is to create the page(s) offline and then upload them to your Internet Service Provider (ISP) via FTP. The second way is to create your web page(s) online using a Telnet program by accessing your UNIX account, if you have one." It later referrs to Windows 95/98, and then to Netscape, the web browser. eh? This page is actuallly a decent resource for learning basic HTML programming, assuming the bright yellow background and flashing animated gifs don't give you siezures.
how to make money
Here we have Grizzly's "How to Make Money Online for Beginners" including the tag-line: "Don't let the stunning graphics and good looks of this blog fool ya'... if you want to know how to make money online... for free... without all the crap... do yourself a favor... get a cup of coffee and do a little reading... Griz." There are a few issues here. One, the blog lacks ANYTHING I would call "stunning graphics," or "good looks." Two... ok, honestly I didn't read it long enough to come up with a second comment. I skimmed through the part informing me that "The Crash Course is designed for beginners just starting out and you can get your feet wet for a buck - a token introductory price for a month just to keep the tire kickers and time wasters away." Then I did myself a favor... got a cup of something that was definitely not coffee, threw a buck in the trash, and went and hung out with some tire kickers and time wasters. It was definitely a better use of a buck than funding this site would have been.
how to make out
hahaha... this takes you to the WikiHow page on how to make out. I'm not linking to it because I don't want to give them any more traffic than they already have. Plus, half the advice is stupid and pointless, and you won't remember or need it once you actually manage to get someone to make out with you. (PS, if my little brother is reading this, you aren't allowed to make out until you are at least 21, hear me?!) I'll just leave you with my favorite piece of advice:
Talk. A little verbal communication will keep things interesting. It's not a good time to start a deep conversation. Just a small phrase in a soft voice will work (especially when accompanied by eye contact and a reassuring smile):
"Are you comfortable?"
"This is amazing."
"Wow."
hahahahahahahahahaha!!!!
how to make a resume
This is boring. But so are resumes.
how to make french toast
Another WikiHow: "Have you ever wondered how to make French Toast? Follow these steps, and you will soon be basking in eggy-bread goodness." I had no idea that enough people wanted to know how to make french toast that it would be on the top ten list. I'm also surprised since french toast is one of the easiest breakfast recipes to make. However, apparently the WikiHow article has been visited 383,363 times, and it has an impressive list of almost 100 authors. Wow. The incompetency of the human race continues to amaze me. This is FRENCH TOAST, people!!! (or "freedom toast" as I prefer to call it) Dip bread in millky egg mixture. Cook. Eat. The end.
how to make a paper airplane
wow, who knew there were so many paper airplanes in the world...
how to make jello shots
This is boring. Who cares about jello shots. It did lead me to this cool idea, of making jello orange slices, though. :)
how to make sushi
Sadly, there's nothing to make fun of here, but don't worry because next we have...
how to make a diaper cake
One word: wtf?!
And now, a bunch more words from a messenger conversation I had with the boyfriend on this topic:
Burfelt says:
diaper cake?
JM says :
hahaha
yeah
that's what I thought
Burfelt says:
I mean seriosuly
JM says:
what kind of a nasty cake is that
Burfelt says:
I don't wanna know
JM says:
it's a cake-shaped arrangement made out of [unused] diapers, apparently
to give someone as a gift like at a baby shower
it's pretty much the stupidest thing I've ever seen
Burfelt says:
hahahahaha
JM says:
I've seen people make them out of towels, too
for wedding gifts
Burfelt says:
Thats SO stupid
Thats like the most insane thing I've ever heard
JM says:
look, if you want to give me diapers, freaking just give me diapers
if you want to give me a cake, give me a dang cake
don't make a CAKE out of DIAPERS
that's like the WORST of both worlds
you don't get a cake, and you have diaper-changing to look forward to
how is that a gift?!!?
Burfelt says:
diaper cakes
It's just plain wrong
I wanna be the fly on the wall in the meeting where that sounded like a good idea
(The link brings you to a YouTube video that will show you step-by-step how to make a diaper cake. The most impressive part of this video is how this woman manages to say the phrase "diaper cake" SO many times and keep a straight face.)
how to make your hair grow faster
well, if you figure this one out, you can sell it, and that will help you out with #2...
sadly, the result is just another boring WikiHow article.
***NEW*** I'm feeling lucky search results included, with commentary...
how to make a website
The result of this search brings up a hideous yellow and blue website entitled "How to Create a Webpage" that SHOULD be called "the perfect example of how NOT to make a webpage," or maybe "If you want absolutely NO ONE to take you seriously, take your webpage-making advice from us!" After close examination, I realized this site is a fossil of the internet days gone by. The first piece of advice for making a website is "There are basically two ways to make a web page. The first way is to create the page(s) offline and then upload them to your Internet Service Provider (ISP) via FTP. The second way is to create your web page(s) online using a Telnet program by accessing your UNIX account, if you have one." It later referrs to Windows 95/98, and then to Netscape, the web browser. eh? This page is actuallly a decent resource for learning basic HTML programming, assuming the bright yellow background and flashing animated gifs don't give you siezures.
how to make money
Here we have Grizzly's "How to Make Money Online for Beginners" including the tag-line: "Don't let the stunning graphics and good looks of this blog fool ya'... if you want to know how to make money online... for free... without all the crap... do yourself a favor... get a cup of coffee and do a little reading... Griz." There are a few issues here. One, the blog lacks ANYTHING I would call "stunning graphics," or "good looks." Two... ok, honestly I didn't read it long enough to come up with a second comment. I skimmed through the part informing me that "The Crash Course is designed for beginners just starting out and you can get your feet wet for a buck - a token introductory price for a month just to keep the tire kickers and time wasters away." Then I did myself a favor... got a cup of something that was definitely not coffee, threw a buck in the trash, and went and hung out with some tire kickers and time wasters. It was definitely a better use of a buck than funding this site would have been.
how to make out
hahaha... this takes you to the WikiHow page on how to make out. I'm not linking to it because I don't want to give them any more traffic than they already have. Plus, half the advice is stupid and pointless, and you won't remember or need it once you actually manage to get someone to make out with you. (PS, if my little brother is reading this, you aren't allowed to make out until you are at least 21, hear me?!) I'll just leave you with my favorite piece of advice:
Talk. A little verbal communication will keep things interesting. It's not a good time to start a deep conversation. Just a small phrase in a soft voice will work (especially when accompanied by eye contact and a reassuring smile):
"Are you comfortable?"
"This is amazing."
"Wow."
hahahahahahahahahaha!!!!
how to make a resume
This is boring. But so are resumes.
how to make french toast
Another WikiHow: "Have you ever wondered how to make French Toast? Follow these steps, and you will soon be basking in eggy-bread goodness." I had no idea that enough people wanted to know how to make french toast that it would be on the top ten list. I'm also surprised since french toast is one of the easiest breakfast recipes to make. However, apparently the WikiHow article has been visited 383,363 times, and it has an impressive list of almost 100 authors. Wow. The incompetency of the human race continues to amaze me. This is FRENCH TOAST, people!!! (or "freedom toast" as I prefer to call it) Dip bread in millky egg mixture. Cook. Eat. The end.
how to make a paper airplane
wow, who knew there were so many paper airplanes in the world...
how to make jello shots
This is boring. Who cares about jello shots. It did lead me to this cool idea, of making jello orange slices, though. :)
how to make sushi
Sadly, there's nothing to make fun of here, but don't worry because next we have...
how to make a diaper cake
One word: wtf?!
And now, a bunch more words from a messenger conversation I had with the boyfriend on this topic:
Burfelt says:
diaper cake?
JM says :
hahaha
yeah
that's what I thought
Burfelt says:
I mean seriosuly
JM says:
what kind of a nasty cake is that
Burfelt says:
I don't wanna know
JM says:
it's a cake-shaped arrangement made out of [unused] diapers, apparently
to give someone as a gift like at a baby shower
it's pretty much the stupidest thing I've ever seen
Burfelt says:
hahahahaha
JM says:
I've seen people make them out of towels, too
for wedding gifts
Burfelt says:
Thats SO stupid
Thats like the most insane thing I've ever heard
JM says:
look, if you want to give me diapers, freaking just give me diapers
if you want to give me a cake, give me a dang cake
don't make a CAKE out of DIAPERS
that's like the WORST of both worlds
you don't get a cake, and you have diaper-changing to look forward to
how is that a gift?!!?
Burfelt says:
diaper cakes
It's just plain wrong
I wanna be the fly on the wall in the meeting where that sounded like a good idea
(The link brings you to a YouTube video that will show you step-by-step how to make a diaper cake. The most impressive part of this video is how this woman manages to say the phrase "diaper cake" SO many times and keep a straight face.)
how to make your hair grow faster
well, if you figure this one out, you can sell it, and that will help you out with #2...
sadly, the result is just another boring WikiHow article.
What the world wants to make
Google search suggestions for "how to make..."
how to make a website
how to make money
how to make out
how to make a resume
how to make french toast
how to make a paper airplane
how to make jello shots
how to make sushi
how to make a diaper cake
how to make your hair grow faster
how to make a website
how to make money
how to make out
how to make a resume
how to make french toast
how to make a paper airplane
how to make jello shots
how to make sushi
how to make a diaper cake
how to make your hair grow faster
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