Category Archives: Mathematics to the rescue

Angry Birds Update

Angry birds peace treaty by Eretz Nehederet


A few years ago I became interested in the question of whather new versions of the computer game “Angry Birds” gradually makes it easier to get high scores. Devoted to the idea of Internet research activity I decided to explore this question on “ARQADE” a Q/A site for video games. I was especially encouraged by the success of an earlier question that was posted there by Andreas Bonini: Is Angry Birds deterministic? As you can see Bonini’s question got 239 upvotes making it the second most popular quastion in the site’s history. (The answer with 322 upvotes may well be the most popular answer!) abd Is Angry Birds deterministic? (Click on pictures to enlarge.) arqaFP

Arqade’s top questions


Some comments to the answer regarding Angry Birds. 

The question if Angry Birds is deterministic is the second most decorated question on Arqade, and its answers were extremely popular as well. (Other decorated questions include: How can I tell if a corpse is safe to eat? How can I kill adorable animals? and  My head keeps falling off. What can I do?.) As you can see from the comments taken from the site referring to science was warmly accepted!

My question

I decided to ask a similar question about new versions and hoped for a similar success. Continue reading

In how many ways you can chose a committee of three students from a class of ten students?

The renewed interest in this old post, reminded me of a more recent event:

Question: In how many ways you can chose a committee of three students from a class of ten students?

My expected answer: {10} \choose {3} which is 120.

Alternative answer 1:(Lior)  There are various ways: you can use majority vote, you can use dictatorship (e.g. the teacher chooses); approval voting, Borda rule…

Alternative answer 2: There are precisely four ways: with repetitions where order does not matter; with repetitions where order matters; without repetitions where order matters; without repetitions where order does not matter,

Alternative answer 3: The number is truly huge. First we need to understand in how many ways we can choose the class of ten students to start with. Should we consider the entire world population? or just the set of all students in the world, or something more delicate? Once we choose the class of ten students we are left with the problem of chosing three among them.

Another way to Revolutionize Football

The angle of Victoria Beckham’s hat (here in a picture from a recent wedding) is closely related to our previous post on football

One of the highlights of the recent Newton Institute  conference on discrete harmonic analysis was a football game which was organized by Frank Barthe and initiated independently by Barthe and Prasad Tetali. There were two teams of 10 players (more or less), I was the oldest player on the field, and it was quite exciting. No spontaneous improvement of my football skills has occurred since my youth.

All the lectures at the conference were videotaped and can be found here. (The football game itself was not videotaped.) Let me mention an idea for a new version of football which occurred to me while playing. For an early suggested football revolution and some subsequent theoretical discussions see this post on football and the intermediate value theorem.

The New Football Game

There are four teams. Team L (the left team), Team R (the right team), Team D (the defense team) and team O (the offense team.)  The left team protects the left goal and tries to score the right goal, the right team protects the right goal and tries to score the left goal, the defense team tries to prevent goals on both sides of the field and the offense team tries to score as much as possible goals on both sides of the field.

In formal terms,  define X to be the number of goals scored to the right and Y the number of goals scored to the left. Then the four teams try to maximize X-Y, Y-X, -X-Y and X+Y, respectively. (I do not assume teams A and B change position at halftime, but the formula can easily be adjusted.)

We can start with five players on each team (but this is negotiable.) Continue reading

Believing that the Earth is Round When it Matters

A world map. Canada seems much bigger than Israel. Note, however, that in the map countries near the equator looks smaller than they are. Update: The round-earth hypothesis is clearer to the people of New Zealand; see the comments section.

One difficult aspect of the academic life is the requirement to fly to conferences and other academic activities all over the world. Strangely, speaking about this hardship to non- academic friends does not always elicit the sympathy we deserve.

Last month, I had to be on duty in two places outside Jerusalem. The first was  a conference in Beijing and the second was a conference and a visit in the the Los Angeles area. My solution was to make a round trip to Beijing and another round trip to LA. (I am simplifying matters since there was some interference due to additional travels, visa matters, etc..)

I discovered the following flaws I make in planning my trips:

1) I am (somewhat) biased toward round trips.

More seriously…

2) I dont take into account that the earth is round.

The book solution to this travel was to go from Jerusalem to Beijing and then from Beijing to Los Angeles and from LA to Jerusalem. I completely ignored this possibility. When I realized it, it made me wonder what this reveals about my true beliefs regarding the round earth hypothesis.

Believing that this coffee cup is a realistic model of the world suffices to prefer the Beijing-LA solution over two round-trips solution!

Continue reading

The Möbius Undershirt

“Look at this brand new undershirt,” my wife said. “I am shaking it and shaking it but still I have this twist.  Can you see what to do?” 

I gave the undershirt a good shake. And another one. And one more. And then it struck me. It was a Möbius undershirt!

What a rare case in which mathematics can come to the rescue in domestic matters

“There is no way in the world this twist can be undone,” I said. “This is a mathematical fact! It is a Möbius undershirt!” My wife listened carefully to my firm statement.

I started to day-dream about the bright future of this rare Möbius undershirt: I will show her to my colleagues!, I will display her in public lectures, and even let some selected graduate students hold her. However, Continue reading

What can the Second Prize Possibly be?


You are guaranteed to win one of the following five prizes, the letter says. (And it is completely free! Just 6 dollars shipping and handling.)

a) a high-definition huge-screen TV,

b) a video camera,

c) a yacht,

d) a decorative ring, and

e) a car.

Oh yeah, you think, a worthless decorative ring, and throw the letter away.

But once I got a letter with the following promise:

You are guaranteed to win two of the following five prizes, the letter said. 

a) a high-definition huge-screen TV,

b) a video camera,

c) a yacht,

d) a decorative ring, and

e) a car.

Now, one prize will be a worthless decorative ring, but what will the second prize be?