Hello and welcome, I’m Nima Amini the author of this mélange.

This blog is intended to collect a set of short (and hopefully interesting) mathematical discussions mainly accessible to an audience possessing basic mathematical literacy (broadly interpreted).

The blog mainly features mathematical puzzles that I have come across and felt necessary to write out somewhere for them not to get lost. Like good jokes, puzzles like to travel by word of mouth and cannot always be traced back to a published source (although for some reason quite a lot of nice puzzles tend to originate with Martin Gardner who wrote the Mathematical Games column in Scientific American from 1956 to 1981).

Most of the puzzles you will see here require no more knowledge than high-school mathematics, but it doesn’t necessarily mean they are easy to solve and will sometimes challenge common intuition.

For puzzles see e.g

YAPP

Antz

The Laser Gun

Games of Chance

Pigeonholes

The blog also contains various other “puzzle-like” discussions that may not be directly posed as problems, but perhaps came about after watching a movie or randomly browsing the internet.

See e.g

The Futurama Problem

Not That Good, Will Hunting

Lowest Unique Bid Auctions

The Resistance

Most solutions are my personal so if you spot any mistakes or would like to see any clarification please do let me know (virtual chocolate bars will be awarded). Likewise if you know any puzzles that you think should be on here don’t hesitate to drop me a comment and I’ll look into it.

Thanks for visiting, I hope you enjoy.

Sweet content! I am quite enjoying perusing the blog. I was a math and business undergrad in college (or I guess Uni to someone in the UK), and the business side sadly left me with little time to delve as deep into my math major as I would have liked. Maybe I will go back for a PhD or something at some point. It’s cool to see an approachable, interesting maths blog to help keep that side of me engaged even though my math academics are on the back burner for now.

~Dylan

Much appreciated Dylan.

Stay involved!

/N

Yeah, this is sweet. I love combinatorics and examinations of probability and logical flaws.

There is some really cool stuff on here.

I’m currently writing a thesis on Pólya counting theory and I’m thinking of using one of your awesome examples if you don’t mind (I’ll credit you of course).

– Seth

Hi, and thank you for taking an interest in this blog.

The examples are standard applications of the theory which I wouldn’t want to take any credit for (you should be able to find most of the examples in standard textbooks). I would also try to be generally cautious about using unreviewed blog posts as resource for an academic thesis.

Good luck in any case!

/N

Cool blog, though you should do something about the layout (fashion police) 😛

I’ve recently been playin The Resistance quite frequently with a group of people and we have also come to the conclusion that the game generally is not fair.

But we found that people often find it difficult to come up with consistent lies if you put a lot of pressure on them, though it is hardly a strategic plan in the mathematical meaning.

By making sure people are forced to talk our group were able to win as the resistance nearly a third of the time, often because someone said something stupid which revealed them.

I was thinking that maybe one can devise a set of questions which a member of the resistance cannot answer consistently without revealing himself and/or hinders him from taking certain actions? Has anyone published anything on this subject recently? Would also be cool if someone took a look at the extended game with further role cards.

Anyway, thanks again for a nice blog (understandable even to me as someone who was never particularly good at math in school).

I believe the game is almost supposed to favour the spies by design, perhaps because it adds to the excitement of the game when the underdogs manage win? Bully tactics is not a mathematical strategy, but I can certainly imagine it being difficult keeping the story straight under high pressure. The game is set up for interrogation in the sense that you can always pose ultimatums such as “If you don’t answer question Q then we are going to assume you are a spy”. Members from both sides are incentivised to answer Q, but it doesn’t mean they cannot lie. I’m not sure how one would logically force any action out of that.

I haven’t seen anything serious published on this game. There are however a few papers on ArXiv discussing the game of Mafia which belongs to the same genre as The Resistance. I suspect the absence of player elimination in The Resistance makes the game more difficult to analyze.

Despite the seeming advantage for the spies there is certainly some power that the resistance can harness from being the majority.The strategy proposed in this blog is essentially an exploit of this to simplify the game by overthrowing the function of the voting system. By using a pre-chosen public decision tree the outcome of the game is determined as soon as the role cards have been dealt out. At least this shows that the spies have no strategy which will yield certain win against any strategy employed by the resistance (which is perhaps obvious in any case by considering the random mission assignment strategy).

Thanks for visiting the blog. I’ll try to do something about the layout when I get time.

/N

Hi Nima. This is Woody. Cool blog! I’ve been trying to find your email address and found this. Send me an email to Woody.lewenstein@gmail.com. I’d love to see you. Woody

Dear Amini Nima,

We need a bidding formula to sell Apartments

Can you provide is with a bidding formula which is not a lottery?

Please contact us to discuss the details

Sincerely

Ozzy