All posts by GreekHouse

The Nation Has Problems, Vol. 4

About Last Month

So as I mentioned last time, both of these have relatively simple solution. For the first problem, calculating probabilities is a pretty futile exercise. You can try it for a small value of n and do it, but if n is--say--1,000,000, things will get out of hand in a hurry. The trick to this problem is just to note that if you throw 2n+1 coins, you will either throw n+1 heads or n+1 tails, but not both. Since the probability of each of these events is the same by symmetry, the probability that either player wins must be exactly 1/2.

Continue reading The Nation Has Problems, Vol. 4

Who’s up for a game of Werewolf?

Since the Twins' season is basically over and today's game is going nowhere fast, I propose we play a game of Werewolf. For those of you who have played Mafia before, it's basically the same game.

If you're interested in playing, send me an email. My email address is (mynamehere)@gmail.com. I'd like to get around 7-9 players. Once we have enough players, I will declare registration over and send you your role via email. For those of you who are werewolves, I will also tell you the identities of your fellow werewolves. Here's how it works:

The goal of the villagers is to kill all the werewolves before they are outnumbered.  If they do so, the villagers are declared the winners (even the villagers who have been killed).  If at any point the werewolves outnumber the villagers during the day, they can simply come out and kill everyone, so they win.  The thing that makes this tricky is that during the day, everybody looks like a villager, so the villagers have no idea who among them is actually a werewolf.  On the other hand, the werewolves know who each other are.

The game consists of two phases--a day phase and a night phase.

DAY PHASE:  Debate begins between everybody in the village and everybody gets to vote for somebody to eliminate.  Once a single player has a majority, I will declare it to be NIGHT.  That player will be killed and his or her role will be revealed.

NIGHT PHASE:  Everybody in the village goes to bed (i.e. no posting is allowed).  The werewolves will select a villager to kill and send the name to me via email.  Once I get a name from the werewolves, I will declare it to be DAY.  That villager's name will be revealed and he will be dead.

Once a player is killed, they are out of the game forever.  So no posting when you're dead!   The game ends when all the werewolves are dead or the werewolves outnumber the villagers during the day.  There are other "special" roles that can be added which add intrigue and complexity to the game.

The actual game will take place over at Spooky's blog.

The Nation Has Problems, Vol.3

About Last Month (err...two months ago)

Again, I'll start by talking about the last post. There is an observation for the first problem that makes it much easier that nobody seemed to pick up on. If you are to apply one of the moves twice, it's the same as not doing it at all! It's clear that this is true if you immediately apply the second move after the first, but even if you apply other moves in between, it won't make a difference. If you want, see if this observation will help you solve the problem, otherwise, I'll finish the solution after the break!

Continue reading The Nation Has Problems, Vol.3

The Nation Has Problems, Vol. 1

Hi everybody!  I'm Dr. House!  (no relation)

Normally, I will just right into my post, but since this is the first post in the series, I'll start out talking about what this series is going to be about and what I want to do with it.

The main point will be for me to introduce you some interesting "math" problems.  I put math in quotes, because as a newly appointed doctor of mathematics, my ideas about what constitutes a math problem differs greatly from someone in the general population (more on this in a bit).  Normally, I'll break these posts into 3 parts:

  1. A recap of results/ideas from the preview volume;
  2. A short essay about a topic of my choosing; and
  3. One, two, or more interesting problems for you all to work on!

Since there is no previous volume to recap today, I'm going to lay the ground rules about what it expected from those that participate.  First off, the purpose of these things is for enjoyment.  I'm not going to be keeping track of how many problems you get right, so if you want to cheat and search the internet, I'm not going to try and stop you, but please be respectful and don't immediately post solutions right below the text for everyone to see.  That being said, I don't want to discourage discussion either!  The point is to have fun and discussing interesting problems is fun!

Continue reading The Nation Has Problems, Vol. 1